LMFDB - Embedded newform 117.2.h.a.22.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(16,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Character	$\chi$	$=$	117.22
Dual form			117.2.h.a.16.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00790 q^{2} +(-1.42488 - 0.984744i) q^{3} +2.03168 q^{4} +(-1.37329 + 2.37860i) q^{5} +(2.86102 + 1.97727i) q^{6} +(1.11905 - 1.93825i) q^{7} -0.0636126 q^{8} +(1.06056 + 2.80628i) q^{9} +(2.75743 - 4.77600i) q^{10} +4.63458 q^{11} +(-2.89490 - 2.00069i) q^{12} +(2.17756 + 2.87372i) q^{13} +(-2.24694 + 3.89182i) q^{14} +(4.29908 - 2.03688i) q^{15} -3.93563 q^{16} +(-0.925543 - 1.60309i) q^{17} +(-2.12950 - 5.63475i) q^{18} +(3.74647 + 6.48908i) q^{19} +(-2.79008 + 4.83256i) q^{20} +(-3.50319 + 1.65979i) q^{21} -9.30580 q^{22} +(-0.948030 - 1.64204i) q^{23} +(0.0906403 + 0.0626421i) q^{24} +(-1.27182 - 2.20287i) q^{25} +(-4.37233 - 5.77015i) q^{26} +(1.25230 - 5.04299i) q^{27} +(2.27355 - 3.93791i) q^{28} -1.71833 q^{29} +(-8.63214 + 4.08986i) q^{30} +(-0.375036 + 0.649582i) q^{31} +8.02960 q^{32} +(-6.60372 - 4.56388i) q^{33} +(1.85840 + 3.21885i) q^{34} +(3.07355 + 5.32354i) q^{35} +(2.15472 + 5.70147i) q^{36} +(1.82852 - 3.16709i) q^{37} +(-7.52256 - 13.0295i) q^{38} +(-0.272883 - 6.23903i) q^{39} +(0.0873583 - 0.151309i) q^{40} +(1.84248 + 3.19128i) q^{41} +(7.03407 - 3.33271i) q^{42} +(-2.05024 + 3.55113i) q^{43} +9.41599 q^{44} +(-8.13147 - 1.33118i) q^{45} +(1.90355 + 3.29705i) q^{46} +(3.36320 + 5.82524i) q^{47} +(5.60780 + 3.87559i) q^{48} +(0.995457 + 1.72418i) q^{49} +(2.55370 + 4.42314i) q^{50} +(-0.259845 + 3.19563i) q^{51} +(4.42410 + 5.83847i) q^{52} +2.52368 q^{53} +(-2.51450 + 10.1258i) q^{54} +(-6.36460 + 11.0238i) q^{55} +(-0.0711856 + 0.123297i) q^{56} +(1.05182 - 12.9355i) q^{57} +3.45024 q^{58} +9.85150 q^{59} +(8.73435 - 4.13829i) q^{60} +(4.78708 - 8.29147i) q^{61} +(0.753037 - 1.30430i) q^{62} +(6.62609 + 1.08474i) q^{63} -8.25141 q^{64} +(-9.82583 + 1.23311i) q^{65} +(13.2596 + 9.16383i) q^{66} +(-6.12861 - 10.6151i) q^{67} +(-1.88041 - 3.25696i) q^{68} +(-0.266158 + 3.27327i) q^{69} +(-6.17139 - 10.6892i) q^{70} +(-7.04017 - 12.1939i) q^{71} +(-0.0674649 - 0.178515i) q^{72} -11.2098 q^{73} +(-3.67149 + 6.35922i) q^{74} +(-0.357062 + 4.39124i) q^{75} +(7.61164 + 13.1837i) q^{76} +(5.18632 - 8.98298i) q^{77} +(0.547923 + 12.5274i) q^{78} +(-0.753706 - 1.30546i) q^{79} +(5.40475 - 9.36130i) q^{80} +(-6.75043 + 5.95245i) q^{81} +(-3.69953 - 6.40778i) q^{82} +(6.58818 + 11.4111i) q^{83} +(-7.11736 + 3.37217i) q^{84} +5.08414 q^{85} +(4.11669 - 7.13032i) q^{86} +(2.44841 + 1.69211i) q^{87} -0.294818 q^{88} +(-2.97704 + 5.15639i) q^{89} +(16.3272 + 2.67289i) q^{90} +(8.00677 - 1.00482i) q^{91} +(-1.92609 - 3.33609i) q^{92} +(1.17405 - 0.556260i) q^{93} +(-6.75299 - 11.6965i) q^{94} -20.5799 q^{95} +(-11.4412 - 7.90710i) q^{96} +(-3.06884 + 5.31539i) q^{97} +(-1.99878 - 3.46199i) q^{98} +(4.91524 + 13.0059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.00790			−1.41980			−0.709901	−	0.704301i	$-0.751261\pi$
$2$	−2.00790			−1.41980			−0.709901	+	0.704301i	$0.751261\pi$
$3$	−1.42488	−	0.984744i	−0.822654	−	0.568542i
$3$	−1.42488	−	0.984744i	−0.822654	−	0.568542i
$4$	2.03168			1.01584
$5$	−1.37329	+	2.37860i	−0.614152	+	1.06374i	0.376381	+	0.926465i	$0.377168\pi$
$5$	−1.37329	+	2.37860i	−0.614152	+	1.06374i	−0.990533	+	0.137277i	$0.956165\pi$
$6$	2.86102	+	1.97727i	1.16801	+	0.807218i
$7$	1.11905	−	1.93825i	0.422961	−	0.732590i	−0.573267	−	0.819369i	$-0.694324\pi$
$7$	1.11905	−	1.93825i	0.422961	−	0.732590i	0.996228	+	0.0867791i	$0.0276574\pi$
$8$	−0.0636126			−0.0224905
$9$	1.06056	+	2.80628i	0.353519	+	0.935427i
$10$	2.75743	−	4.77600i	0.871975	−	1.51030i
$11$	4.63458			1.39738			0.698689	−	0.715425i	$-0.253767\pi$
$11$	4.63458			1.39738			0.698689	+	0.715425i	$0.253767\pi$
$12$	−2.89490	−	2.00069i	−0.835685	−	0.577548i
$13$	2.17756	+	2.87372i	0.603946	+	0.797025i
$13$	2.17756	+	2.87372i	0.603946	+	0.797025i
$14$	−2.24694	+	3.89182i	−0.600521	+	1.04013i
$15$	4.29908	−	2.03688i	1.11002	−	0.525921i
$16$	−3.93563			−0.983909
$17$	−0.925543	−	1.60309i	−0.224477	−	0.388806i	0.731685	−	0.681643i	$-0.238734\pi$
$17$	−0.925543	−	1.60309i	−0.224477	−	0.388806i	−0.956162	+	0.292837i	$0.905401\pi$
$18$	−2.12950	−	5.63475i	−0.501928	−	1.32812i
$19$	3.74647	+	6.48908i	0.859500	+	1.48870i	0.872407	+	0.488781i	$0.162558\pi$
$19$	3.74647	+	6.48908i	0.859500	+	1.48870i	−0.0129070	+	0.999917i	$0.504109\pi$
$20$	−2.79008	+	4.83256i	−0.623880	+	1.08059i
$21$	−3.50319	+	1.65979i	−0.764459	+	0.362197i
$22$	−9.30580			−1.98400
$23$	−0.948030	−	1.64204i	−0.197678	−	0.342388i	0.750097	−	0.661328i	$-0.230007\pi$
$23$	−0.948030	−	1.64204i	−0.197678	−	0.342388i	−0.947775	+	0.318939i	$0.896673\pi$
$24$	0.0906403	+	0.0626421i	0.0185019	+	0.0127868i
$25$	−1.27182	−	2.20287i	−0.254365	−	0.440573i
$26$	−4.37233	−	5.77015i	−0.857484	−	1.13162i
$27$	1.25230	−	5.04299i	0.241006	−	0.970524i
$28$	2.27355	−	3.93791i	0.429661	−	0.744194i
$29$	−1.71833			−0.319086			−0.159543	−	0.987191i	$-0.551002\pi$
$29$	−1.71833			−0.319086			−0.159543	+	0.987191i	$0.551002\pi$
$30$	−8.63214	+	4.08986i	−1.57601	+	0.746704i
$31$	−0.375036	+	0.649582i	−0.0673585	+	0.116668i	−0.897738	−	0.440530i	$-0.854790\pi$
$31$	−0.375036	+	0.649582i	−0.0673585	+	0.116668i	0.830379	+	0.557199i	$0.188124\pi$
$32$	8.02960			1.41945
$33$	−6.60372	−	4.56388i	−1.14956	−	0.794469i
$34$	1.85840	+	3.21885i	0.318713	+	0.552028i
$35$	3.07355	+	5.32354i	0.519524	+	0.899843i
$36$	2.15472	+	5.70147i	0.359119	+	0.950245i
$37$	1.82852	−	3.16709i	0.300607	−	0.520666i	−0.675667	−	0.737207i	$-0.736144\pi$
$37$	1.82852	−	3.16709i	0.300607	−	0.520666i	0.976274	+	0.216541i	$0.0694774\pi$
$38$	−7.52256	−	13.0295i	−1.22032	−	2.11366i
$39$	−0.272883	−	6.23903i	−0.0436962	−	0.999045i
$40$	0.0873583	−	0.151309i	0.0138126	−	0.0239240i
$41$	1.84248	+	3.19128i	0.287748	+	0.498393i	0.973272	−	0.229656i	$-0.0737602\pi$
$41$	1.84248	+	3.19128i	0.287748	+	0.498393i	−0.685524	+	0.728050i	$0.740427\pi$
$42$	7.03407	−	3.33271i	1.08538	−	0.514248i
$43$	−2.05024	+	3.55113i	−0.312659	+	0.541542i	−0.978937	−	0.204162i	$-0.934553\pi$
$43$	−2.05024	+	3.55113i	−0.312659	+	0.541542i	0.666278	+	0.745703i	$0.267886\pi$
$44$	9.41599			1.41951
$45$	−8.13147	−	1.33118i	−1.21217	−	0.198441i
$46$	1.90355	+	3.29705i	0.280664	+	0.486124i
$47$	3.36320	+	5.82524i	0.490573	+	0.849698i	0.999941	−	0.0108509i	$-0.00345403\pi$
$47$	3.36320	+	5.82524i	0.490573	+	0.849698i	−0.509368	+	0.860549i	$0.670121\pi$
$48$	5.60780	+	3.87559i	0.809416	+	0.559394i
$49$	0.995457	+	1.72418i	0.142208	+	0.246312i
$50$	2.55370	+	4.42314i	0.361148	+	0.625527i
$51$	−0.259845	+	3.19563i	−0.0363855	+	0.447478i
$52$	4.42410	+	5.83847i	0.613513	+	0.809650i
$53$	2.52368			0.346654			0.173327	−	0.984864i	$-0.444548\pi$
$53$	2.52368			0.346654			0.173327	+	0.984864i	$0.444548\pi$
$54$	−2.51450	+	10.1258i	−0.342181	+	1.37795i
$55$	−6.36460	+	11.0238i	−0.858203	+	1.48645i
$56$	−0.0711856	+	0.123297i	−0.00951258	+	0.0164763i
$57$	1.05182	−	12.9355i	0.139316	−	1.71334i
$58$	3.45024			0.453039
$59$	9.85150			1.28256			0.641278	−	0.767309i	$-0.278405\pi$
$59$	9.85150			1.28256			0.641278	+	0.767309i	$0.278405\pi$
$60$	8.73435	−	4.13829i	1.12760	−	0.534251i
$61$	4.78708	−	8.29147i	0.612923	−	1.06161i	−0.377822	−	0.925878i	$-0.623327\pi$
$61$	4.78708	−	8.29147i	0.612923	−	1.06161i	0.990745	−	0.135736i	$-0.0433397\pi$
$62$	0.753037	−	1.30430i	0.0956358	−	0.165646i
$63$	6.62609	+	1.08474i	0.834809	+	0.136664i
$64$	−8.25141			−1.03143
$65$	−9.82583	+	1.23311i	−1.21874	+	0.152948i
$66$	13.2596	+	9.16383i	1.63215	+	1.12799i
$67$	−6.12861	−	10.6151i	−0.748728	−	1.29684i	−0.948432	−	0.316979i	$-0.897331\pi$
$67$	−6.12861	−	10.6151i	−0.748728	−	1.29684i	0.199704	−	0.979856i	$-0.436002\pi$
$68$	−1.88041	−	3.25696i	−0.228033	−	0.394965i
$69$	−0.266158	+	3.27327i	−0.0320416	+	0.394055i
$70$	−6.17139	−	10.6892i	−0.737622	−	1.27760i
$71$	−7.04017	−	12.1939i	−0.835514	−	1.44715i	−0.893611	−	0.448842i	$-0.851837\pi$
$71$	−7.04017	−	12.1939i	−0.835514	−	1.44715i	0.0580970	−	0.998311i	$-0.481497\pi$
$72$	−0.0674649	−	0.178515i	−0.00795081	−	0.0210382i
$73$	−11.2098			−1.31200			−0.656001	−	0.754760i	$-0.727753\pi$
$73$	−11.2098			−1.31200			−0.656001	+	0.754760i	$0.727753\pi$
$74$	−3.67149	+	6.35922i	−0.426803	+	0.739244i
$75$	−0.357062	+	4.39124i	−0.0412300	+	0.507056i
$76$	7.61164	+	13.1837i	0.873115	+	1.51228i
$77$	5.18632	−	8.98298i	0.591037	−	1.02371i
$78$	0.547923	+	12.5274i	0.0620400	+	1.41845i
$79$	−0.753706	−	1.30546i	−0.0847985	−	0.146875i	0.820507	−	0.571637i	$-0.193691\pi$
$79$	−0.753706	−	1.30546i	−0.0847985	−	0.146875i	−0.905305	+	0.424761i	$0.860358\pi$
$80$	5.40475	−	9.36130i	0.604269	−	1.04663i
$81$	−6.75043	+	5.95245i	−0.750048	+	0.661383i
$82$	−3.69953	−	6.40778i	−0.408545	−	0.707621i
$83$	6.58818	+	11.4111i	0.723146	+	1.25253i	0.959732	+	0.280916i	$0.0906382\pi$
$83$	6.58818	+	11.4111i	0.723146	+	1.25253i	−0.236586	+	0.971611i	$0.576028\pi$
$84$	−7.11736	+	3.37217i	−0.776568	+	0.367934i
$85$	5.08414			0.551452
$86$	4.11669	−	7.13032i	0.443914	−	0.768882i
$87$	2.44841	+	1.69211i	0.262497	+	0.181414i
$88$	−0.294818			−0.0314277
$89$	−2.97704	+	5.15639i	−0.315566	+	0.546576i	−0.979558	−	0.201164i	$-0.935528\pi$
$89$	−2.97704	+	5.15639i	−0.315566	+	0.546576i	0.663992	+	0.747740i	$0.268861\pi$
$90$	16.3272	+	2.67289i	1.72104	+	0.281747i
$91$	8.00677	−	1.00482i	0.839338	−	0.105334i
$92$	−1.92609	−	3.33609i	−0.200809	−	0.347812i
$93$	1.17405	−	0.556260i	0.121744	−	0.0576815i
$94$	−6.75299	−	11.6965i	−0.696518	−	1.20640i
$95$	−20.5799			−2.11145
$96$	−11.4412	−	7.90710i	−1.16771	−	0.807015i
$97$	−3.06884	+	5.31539i	−0.311594	+	0.539697i	−0.978708	−	0.205259i	$-0.934196\pi$
$97$	−3.06884	+	5.31539i	−0.311594	+	0.539697i	0.667114	+	0.744956i	$0.267530\pi$
$98$	−1.99878	−	3.46199i	−0.201908	−	0.349714i
$99$	4.91524	+	13.0059i	0.494001	+	1.30715i
$100$	−2.58394	−	4.47552i	−0.258394	−	0.447552i
$101$	−9.43261			−0.938579			−0.469290	−	0.883044i	$-0.655490\pi$
$101$	−9.43261			−0.938579			−0.469290	+	0.883044i	$0.655490\pi$
$102$	0.521743	−	6.41652i	0.0516603	−	0.635330i
$103$	1.32937	−	2.30254i	0.130987	−	0.226876i	−0.793070	−	0.609130i	$-0.791519\pi$
$103$	1.32937	−	2.30254i	0.130987	−	0.226876i	0.924057	+	0.382254i	$0.124852\pi$
$104$	−0.138520	−	0.182805i	−0.0135830	−	0.0179255i
$105$	0.862893	−	10.6121i	0.0842097	−	1.03563i
$106$	−5.06730			−0.492180
$107$	−0.149595	+	0.259106i	−0.0144619	+	0.0250487i	−0.873166	−	0.487423i	$-0.837937\pi$
$107$	−0.149595	+	0.259106i	−0.0144619	+	0.0250487i	0.858704	+	0.512472i	$0.171270\pi$
$108$	2.54428	−	10.2457i	0.244823	−	0.985897i
$109$	0.708224			0.0678356			0.0339178	−	0.999425i	$-0.489202\pi$
$109$	0.708224			0.0678356			0.0339178	+	0.999425i	$0.489202\pi$
$110$	12.7795	−	22.1348i	1.21848	−	2.11047i
$111$	−5.72419	+	2.71209i	−0.543316	+	0.257421i
$112$	−4.40417	+	7.62824i	−0.416155	+	0.720801i
$113$	−8.74797			−0.822940			−0.411470	−	0.911423i	$-0.634985\pi$
$113$	−8.74797			−0.822940			−0.411470	+	0.911423i	$0.634985\pi$
$114$	−2.11194	+	25.9732i	−0.197802	+	2.43261i
$115$	5.20766			0.485617
$116$	−3.49110			−0.324140
$117$	−5.75503	+	9.15858i	−0.532052	+	0.846711i
$118$	−19.7809			−1.82098
$119$	−4.14291			−0.379780
$120$	−0.273476	+	0.129571i	−0.0249648	+	0.0118282i
$121$	10.4793			0.952668
$122$	−9.61200	+	16.6485i	−0.870230	+	1.50728i
$123$	0.517274	−	6.36155i	0.0466410	−	0.573602i
$124$	−0.761954	+	1.31974i	−0.0684255	+	0.118516i
$125$	−6.74654			−0.603429
$126$	−13.3046	−	2.17805i	−1.18526	−	0.194037i
$127$	9.01640	−	15.6169i	0.800076	−	1.38577i	−0.119489	−	0.992836i	$-0.538126\pi$
$127$	9.01640	−	15.6169i	0.800076	−	1.38577i	0.919565	−	0.392938i	$-0.128541\pi$
$128$	0.508837			0.0449753
$129$	6.41830	−	3.04096i	0.565100	−	0.267741i
$130$	19.7293	−	2.47597i	1.73038	−	0.217157i
$131$	5.30430	−	9.18731i	0.463438	−	0.802699i	−0.535691	−	0.844414i	$-0.679949\pi$
$131$	5.30430	−	9.18731i	0.463438	−	0.802699i	0.999130	+	0.0417151i	$0.0132822\pi$
$132$	−13.4166	−	9.27234i	−1.16777	−	0.807054i
$133$	16.7700			1.45414
$134$	12.3057	+	21.3140i	1.06305	+	1.84125i
$135$	10.2755	+	9.90419i	0.884373	+	0.852417i
$136$	0.0588762	+	0.101977i	0.00504859	+	0.00874442i
$137$	−2.97372	+	5.15063i	−0.254062	+	0.440048i	−0.964640	−	0.263570i	$-0.915100\pi$
$137$	−2.97372	+	5.15063i	−0.254062	+	0.440048i	0.710578	+	0.703618i	$0.248433\pi$
$138$	0.534419	−	6.57241i	0.0454928	−	0.559481i
$139$	−13.7776			−1.16860			−0.584300	−	0.811538i	$-0.698631\pi$
$139$	−13.7776			−1.16860			−0.584300	+	0.811538i	$0.698631\pi$
$140$	6.24447	+	10.8157i	0.527754	+	0.914097i
$141$	0.944213	−	11.6121i	0.0795170	−	0.977919i
$142$	14.1360	+	24.4842i	1.18627	+	2.05467i
$143$	10.0921	+	13.3185i	0.843941	+	1.11375i
$144$	−4.17397	−	11.0445i	−0.347831	−	0.920375i
$145$	2.35976	−	4.08722i	0.195967	−	0.339425i
$146$	22.5081			1.86278
$147$	0.279473	−	3.43702i	0.0230505	−	0.283481i
$148$	3.71497	−	6.43452i	0.305369	−	0.528914i
$149$	10.8144			0.885948			0.442974	−	0.896535i	$-0.353923\pi$
$149$	10.8144			0.885948			0.442974	+	0.896535i	$0.353923\pi$
$150$	0.716947	−	8.81719i	0.0585385	−	0.719920i
$151$	−6.45173	−	11.1747i	−0.525035	−	0.909387i	−0.999575	−	0.0291528i	$-0.990719\pi$
$151$	−6.45173	−	11.1747i	−0.525035	−	0.909387i	0.474540	−	0.880234i	$-0.342614\pi$
$152$	−0.238323	−	0.412787i	−0.0193305	−	0.0334815i
$153$	3.51712	−	4.29750i	0.284343	−	0.347432i
$154$	−10.4136	+	18.0370i	−0.839156	+	1.45346i
$155$	−1.03006	−	1.78412i	−0.0827367	−	0.143304i
$156$	−0.554411	−	12.6757i	−0.0443884	−	1.01487i
$157$	−4.22692	+	7.32124i	−0.337345	+	0.584298i	−0.983932	−	0.178541i	$-0.942862\pi$
$157$	−4.22692	+	7.32124i	−0.337345	+	0.584298i	0.646588	+	0.762840i	$0.276195\pi$
$158$	1.51337	+	2.62123i	0.120397	+	0.208534i
$159$	−3.59593	−	2.48518i	−0.285176	−	0.197087i
$160$	−11.0269	+	19.0992i	−0.871756	+	1.50993i
$161$	−4.24357			−0.334440
$162$	13.5542	−	11.9520i	1.06492	−	0.939034i
$163$	12.0242	+	20.8266i	0.941810	+	1.63126i	0.762016	+	0.647558i	$0.224210\pi$
$163$	12.0242	+	20.8266i	0.941810	+	1.63126i	0.179794	+	0.983704i	$0.442457\pi$
$164$	3.74334	+	6.48365i	0.292306	+	0.506288i
$165$	19.9244	−	9.44009i	1.55111	−	0.734910i
$166$	−13.2284	−	22.9123i	−1.02673	−	1.77834i
$167$	−4.75638	−	8.23829i	−0.368060	−	0.637498i	0.621202	−	0.783650i	$-0.286644\pi$
$167$	−4.75638	−	8.23829i	−0.368060	−	0.637498i	−0.989262	+	0.146152i	$0.953311\pi$
$168$	0.222847	−	0.105584i	0.0171930	−	0.00814597i
$169$	−3.51648	+	12.5154i	−0.270498	+	0.962720i
$170$	−10.2085			−0.782954
$171$	−14.2368	+	17.3957i	−1.08872	+	1.33028i
$172$	−4.16544	+	7.21475i	−0.317612	+	0.550120i
$173$	5.73435	−	9.93218i	0.435975	−	0.755130i	−0.561400	−	0.827545i	$-0.689737\pi$
$173$	5.73435	−	9.93218i	0.435975	−	0.755130i	0.997375	+	0.0724145i	$0.0230704\pi$
$174$	−4.91618	−	3.39761i	−0.372694	−	0.257572i
$175$	−5.69294			−0.430346
$176$	−18.2400			−1.37489
$177$	−14.0372	−	9.70120i	−1.05510	−	0.729187i
$178$	5.97762	−	10.3535i	0.448041	−	0.776031i
$179$	5.26198	−	9.11402i	0.393299	−	0.681214i	−0.599583	−	0.800312i	$-0.704667\pi$
$179$	5.26198	−	9.11402i	0.393299	−	0.681214i	0.992882	+	0.119098i	$0.0380004\pi$
$180$	−16.5206	−	2.70454i	−1.23137	−	0.201584i
$181$	11.0530			0.821566			0.410783	−	0.911733i	$-0.365255\pi$
$181$	11.0530			0.821566			0.410783	+	0.911733i	$0.365255\pi$
$182$	−16.0768	+	2.01759i	−1.19169	+	0.149554i
$183$	−14.9860	+	7.10029i	−1.10780	+	0.524868i
$184$	0.0603067	+	0.104454i	0.00444587	+	0.00770047i
$185$	5.02216	+	8.69864i	0.369237	+	0.639537i
$186$	−2.35739	+	1.11692i	−0.172852	+	0.0818964i
$187$	−4.28950	−	7.42964i	−0.313680	−	0.543309i
$188$	6.83295	+	11.8350i	0.498344	+	0.863158i
$189$	−8.37319	−	8.07063i	−0.609060	−	0.587052i
$190$	41.3225			2.99785
$191$	9.86785	−	17.0916i	0.714012	−	1.23671i	−0.249327	−	0.968419i	$-0.580209\pi$
$191$	9.86785	−	17.0916i	0.714012	−	1.23671i	0.963339	−	0.268286i	$-0.0864573\pi$
$192$	11.7573	+	8.12553i	0.848507	+	0.586409i
$193$	−5.36757	−	9.29691i	−0.386366	−	0.669206i	0.605591	−	0.795776i	$-0.292937\pi$
$193$	−5.36757	−	9.29691i	−0.386366	−	0.669206i	−0.991958	+	0.126570i	$0.959603\pi$
$194$	6.16195	−	10.6728i	0.442402	−	0.766263i
$195$	15.2149	+	7.91889i	1.08956	+	0.567084i
$196$	2.02245	+	3.50299i	0.144461	+	0.250213i
$197$	−9.88808	+	17.1267i	−0.704497	+	1.22022i	0.262376	+	0.964966i	$0.415494\pi$
$197$	−9.88808	+	17.1267i	−0.704497	+	1.22022i	−0.966873	+	0.255258i	$0.917839\pi$
$198$	−9.86934	−	26.1147i	−0.701383	−	1.85589i
$199$	−4.56054	−	7.89908i	−0.323288	−	0.559951i	0.657876	−	0.753126i	$-0.271455\pi$
$199$	−4.56054	−	7.89908i	−0.323288	−	0.559951i	−0.981164	+	0.193175i	$0.938122\pi$
$200$	0.0809041	+	0.140130i	0.00572078	+	0.00990869i
$201$	−1.72059	+	21.1603i	−0.121361	+	1.49253i
$202$	18.9398			1.33260
$203$	−1.92290	+	3.33055i	−0.134961	+	0.233759i
$204$	−0.527921	+	6.49250i	−0.0369619	+	0.454566i
$205$	−10.1210			−0.706883
$206$	−2.66925	+	4.62327i	−0.185975	+	0.322119i
$207$	3.60257	−	4.40191i	0.250396	−	0.305954i
$208$	−8.57007	−	11.3099i	−0.594228	−	0.784200i
$209$	17.3633	+	30.0742i	1.20105	+	2.08027i
$210$	−1.73261	+	21.3080i	−0.119561	+	1.47039i
$211$	−0.664016	−	1.15011i	−0.0457127	−	0.0791768i	0.842264	−	0.539066i	$-0.181223\pi$
$211$	−0.664016	−	1.15011i	−0.0457127	−	0.0791768i	−0.887976	+	0.459889i	$0.847889\pi$
$212$	5.12731			0.352145
$213$	−1.97651	+	24.3076i	−0.135428	+	1.66553i
$214$	0.300372	−	0.520260i	0.0205330	−	0.0355642i
$215$	−5.63114	−	9.75342i	−0.384040	−	0.665178i
$216$	−0.0796622	+	0.320798i	−0.00542033	+	0.0218275i
$217$	0.839368	+	1.45383i	0.0569800	+	0.0986923i
$218$	−1.42205			−0.0963131
$219$	15.9725	+	11.0387i	1.07932	+	0.745929i
$220$	−12.9308	+	22.3969i	−0.871797	+	1.51000i
$221$	2.59139	−	6.15056i	0.174316	−	0.413732i
$222$	11.4936	−	5.44563i	0.771402	−	0.365487i
$223$	7.10340			0.475679			0.237839	−	0.971304i	$-0.423561\pi$
$223$	7.10340			0.475679			0.237839	+	0.971304i	$0.423561\pi$
$224$	8.98552	−	15.5634i	0.600370	−	1.03987i
$225$	4.83302	−	5.90537i	0.322201	−	0.393691i
$226$	17.5651			1.16841
$227$	4.90104	−	8.48884i	0.325293	−	0.563424i	−0.656278	−	0.754519i	$-0.727870\pi$
$227$	4.90104	−	8.48884i	0.325293	−	0.563424i	0.981572	+	0.191094i	$0.0612037\pi$
$228$	2.13695	−	26.2807i	0.141523	−	1.74049i
$229$	0.141350	−	0.244825i	0.00934064	−	0.0161785i	−0.861317	−	0.508067i	$-0.830360\pi$
$229$	0.141350	−	0.244825i	0.00934064	−	0.0161785i	0.870658	+	0.491889i	$0.163693\pi$
$230$	−10.4565			−0.689481
$231$	−16.2358	+	7.69245i	−1.06824	+	0.506126i
$232$	0.109307			0.00717638
$233$	−24.9871			−1.63696			−0.818478	−	0.574537i	$-0.805182\pi$
$233$	−24.9871			−1.63696			−0.818478	+	0.574537i	$0.805182\pi$
$234$	11.5555	−	18.3896i	0.755410	−	1.20216i
$235$	−18.4745			−1.20515
$236$	20.0151			1.30287
$237$	−0.211601	+	2.60232i	−0.0137450	+	0.169039i
$238$	8.31858			0.539213
$239$	3.85548	−	6.67788i	0.249390	−	0.431956i	−0.713967	−	0.700180i	$-0.753103\pi$
$239$	3.85548	−	6.67788i	0.249390	−	0.431956i	0.963357	+	0.268223i	$0.0864365\pi$
$240$	−16.9196	+	8.01642i	−1.09216	+	0.517458i
$241$	15.0878	−	26.1328i	0.971891	−	1.68336i	0.282056	−	0.959398i	$-0.408983\pi$
$241$	15.0878	−	26.1328i	0.971891	−	1.68336i	0.689835	−	0.723967i	$-0.257683\pi$
$242$	−21.0415			−1.35260
$243$	15.4802	−	1.83407i	0.993054	−	0.117656i
$244$	9.72582	−	16.8456i	0.622632	−	1.07843i
$245$	−5.46819			−0.349350
$246$	−1.03864	+	12.7734i	−0.0662210	+	0.814402i
$247$	−10.4896	+	24.8966i	−0.667438	+	1.58414i
$248$	0.0238570	−	0.0413216i	0.00151492	−	0.00262392i
$249$	1.84962	−	22.7470i	0.117215	−	1.44154i
$250$	13.5464			0.856750
$251$	−1.94008	−	3.36031i	−0.122456	−	0.212101i	0.798279	−	0.602287i	$-0.205744\pi$
$251$	−1.94008	−	3.36031i	−0.122456	−	0.212101i	−0.920736	+	0.390187i	$0.872411\pi$
$252$	13.4621	+	2.20385i	0.848033	+	0.138829i
$253$	−4.39372	−	7.61015i	−0.276231	−	0.478446i
$254$	−18.1041	+	31.3572i	−1.13595	+	1.96752i
$255$	−7.24428	−	5.00658i	−0.453654	−	0.313524i
$256$	15.4811			0.967570
$257$	3.83954	+	6.65028i	0.239504	+	0.414833i	0.960572	−	0.278031i	$-0.0896819\pi$
$257$	3.83954	+	6.65028i	0.239504	+	0.414833i	−0.721068	+	0.692864i	$0.756349\pi$
$258$	−12.8873	+	6.10595i	−0.802330	+	0.380140i
$259$	−4.09241	−	7.08826i	−0.254290	−	0.440443i
$260$	−19.9629	+	2.50529i	−1.23805	+	0.155371i
$261$	−1.82239	−	4.82212i	−0.112803	−	0.298482i
$262$	−10.6505	+	18.4472i	−0.657991	+	1.13967i
$263$	−9.96367			−0.614386			−0.307193	−	0.951647i	$-0.599390\pi$
$263$	−9.96367			−0.614386			−0.307193	+	0.951647i	$0.599390\pi$
$264$	0.420080	+	0.290320i	0.0258541	+	0.0178680i
$265$	−3.46573	+	6.00282i	−0.212898	+	0.368750i
$266$	−33.6725			−2.06459
$267$	9.31965	−	4.41560i	0.570353	−	0.270231i
$268$	−12.4514	−	21.5664i	−0.760589	−	1.31738i
$269$	−2.44660	−	4.23764i	−0.149172	−	0.258373i	0.781750	−	0.623592i	$-0.214327\pi$
$269$	−2.44660	−	4.23764i	−0.149172	−	0.258373i	−0.930922	+	0.365219i	$0.880994\pi$
$270$	−20.6322	−	19.8867i	−1.25564	−	1.21026i
$271$	2.64931	−	4.58874i	0.160934	−	0.278746i	−0.774270	−	0.632856i	$-0.781883\pi$
$271$	2.64931	−	4.58874i	0.160934	−	0.278746i	0.935204	+	0.354109i	$0.115216\pi$
$272$	3.64260	+	6.30917i	0.220865	+	0.382549i
$273$	−12.3982	−	6.45287i	−0.750372	−	0.390546i
$274$	5.97094	−	10.3420i	0.360718	−	0.624782i
$275$	−5.89438	−	10.2094i	−0.355444	−	0.615647i
$276$	−0.540747	+	6.65024i	−0.0325492	+	0.400297i
$277$	−1.33857	+	2.31847i	−0.0804268	+	0.139303i	−0.903433	−	0.428729i	$-0.858962\pi$
$277$	−1.33857	+	2.31847i	−0.0804268	+	0.139303i	0.823007	+	0.568032i	$0.192295\pi$
$278$	27.6641			1.65918
$279$	−2.22066	−	0.363538i	−0.132947	−	0.0217644i
$280$	−0.195516	−	0.338644i	−0.0116843	−	0.0202379i
$281$	−1.11317	−	1.92806i	−0.0664059	−	0.115018i	0.830911	−	0.556406i	$-0.187820\pi$
$281$	−1.11317	−	1.92806i	−0.0664059	−	0.115018i	−0.897317	+	0.441387i	$0.854487\pi$
$282$	−1.89589	+	23.3161i	−0.112899	+	1.38845i
$283$	1.28374	+	2.22350i	0.0763102	+	0.132173i	0.901655	−	0.432455i	$-0.142353\pi$
$283$	1.28374	+	2.22350i	0.0763102	+	0.132173i	−0.825345	+	0.564629i	$0.809019\pi$
$284$	−14.3034	−	24.7742i	−0.848749	−	1.47008i
$285$	29.3239	+	20.2659i	1.73700	+	1.20045i
$286$	−20.2639	−	26.7422i	−1.19823	−	1.58130i
$287$	8.24732			0.486824
$288$	8.51586	+	22.5333i	0.501802	+	1.32779i
$289$	6.78674	−	11.7550i	0.399220	−	0.691469i
$290$	−4.73817	+	8.20674i	−0.278235	+	0.481917i
$291$	9.60703	−	4.55177i	0.563174	−	0.266829i
$292$	−22.7746			−1.33278
$293$	−1.40062			−0.0818251			−0.0409125	−	0.999163i	$-0.513027\pi$
$293$	−1.40062			−0.0818251			−0.0409125	+	0.999163i	$0.513027\pi$
$294$	−0.561155	+	6.90121i	−0.0327272	+	0.402487i
$295$	−13.5289	+	23.4328i	−0.787684	+	1.36431i
$296$	−0.116317	+	0.201467i	−0.00676079	+	0.0117100i
$297$	5.80390	−	23.3721i	0.336776	−	1.35619i
$298$	−21.7142			−1.25787
$299$	2.65435	−	6.30000i	0.153505	−	0.364338i
$300$	−0.725437	+	8.92160i	−0.0418831	+	0.515089i
$301$	4.58865	+	7.94777i	0.264485	+	0.458102i
$302$	12.9545	+	22.4378i	0.745446	+	1.29115i
$303$	13.4403	+	9.28870i	0.772126	+	0.533622i
$304$	−14.7447	−	25.5386i	−0.845669	−	1.46474i
$305$	13.1481	+	22.7731i	0.752856	+	1.30398i
$306$	−7.06205	+	8.62898i	−0.403710	+	0.493286i
$307$	−18.2734			−1.04292			−0.521460	−	0.853276i	$-0.674612\pi$
$307$	−18.2734			−1.04292			−0.521460	+	0.853276i	$0.674612\pi$
$308$	10.5370	−	18.2505i	0.600399	−	1.03992i
$309$	−4.16160	+	1.97175i	−0.236745	+	0.112169i
$310$	2.06827	+	3.58235i	0.117470	+	0.203464i
$311$	−3.14615	+	5.44929i	−0.178402	+	0.309001i	−0.941333	−	0.337478i	$-0.890426\pi$
$311$	−3.14615	+	5.44929i	−0.178402	+	0.309001i	0.762931	+	0.646479i	$0.223759\pi$
$312$	0.0173588	+	0.396881i	0.000982748	+	0.0224690i
$313$	10.5551	+	18.2820i	0.596612	+	1.03336i	0.993317	+	0.115416i	$0.0368202\pi$
$313$	10.5551	+	18.2820i	0.596612	+	1.03336i	−0.396705	+	0.917946i	$0.629846\pi$
$314$	8.48725	−	14.7003i	0.478963	−	0.829588i
$315$	−11.6797	+	14.2712i	−0.658075	+	0.804089i
$316$	−1.53129	−	2.65227i	−0.0861418	−	0.149202i
$317$	−4.75705	−	8.23946i	−0.267183	−	0.462774i	0.700950	−	0.713210i	$-0.252759\pi$
$317$	−4.75705	−	8.23946i	−0.267183	−	0.462774i	−0.968133	+	0.250436i	$0.919426\pi$
$318$	7.22029	+	4.99000i	0.404894	+	0.279825i
$319$	−7.96374			−0.445884
$320$	11.3315	−	19.6268i	0.633452	−	1.09717i
$321$	0.468307	−	0.221882i	0.0261384	−	0.0123842i
$322$	8.52068			0.474839
$323$	6.93504	−	12.0118i	0.385876	−	0.668357i
$324$	−13.7147	+	12.0935i	−0.761929	+	0.671860i
$325$	3.56093	−	8.45173i	0.197525	−	0.468818i
$326$	−24.1435	−	41.8178i	−1.33718	−	2.31607i
$327$	−1.00913	−	0.697419i	−0.0558052	−	0.0385674i
$328$	−0.117205	−	0.203005i	−0.00647157	−	0.0112091i
$329$	15.0544			0.829973
$330$	−40.0063	+	18.9548i	−2.20228	+	1.04343i
$331$	−3.12981	+	5.42098i	−0.172030	+	0.297964i	−0.939129	−	0.343564i	$-0.888366\pi$
$331$	−3.12981	+	5.42098i	−0.172030	+	0.297964i	0.767100	+	0.641528i	$0.221699\pi$
$332$	13.3851	+	23.1836i	0.734601	+	1.27237i
$333$	10.8270	+	1.77246i	0.593316	+	0.0971302i
$334$	9.55036	+	16.5417i	0.522572	+	0.905122i
$335$	33.6653			1.83933
$336$	13.7873	−	6.53234i	0.752157	−	0.356369i
$337$	3.09213	−	5.35572i	0.168439	−	0.291745i	−0.769432	−	0.638728i	$-0.779461\pi$
$337$	3.09213	−	5.35572i	0.168439	−	0.291745i	0.937871	+	0.346984i	$0.112794\pi$
$338$	7.06075	−	25.1297i	0.384054	−	1.36687i
$339$	12.4648	+	8.61451i	0.676995	+	0.467876i
$340$	10.3293			0.560188
$341$	−1.73814	+	3.01054i	−0.0941253	+	0.163030i
$342$	28.5862	−	34.9289i	1.54577	−	1.88874i
$343$	20.1226			1.08652
$344$	0.130421	−	0.225896i	0.00703185	−	0.0121795i
$345$	−7.42029	−	5.12821i	−0.399495	−	0.276094i
$346$	−11.5140	+	19.9429i	−0.618998	+	1.07214i
$347$	7.38405			0.396397			0.198198	−	0.980162i	$-0.436491\pi$
$347$	7.38405			0.396397			0.198198	+	0.980162i	$0.436491\pi$
$348$	4.97439	+	3.43784i	0.266655	+	0.184287i
$349$	−30.1213			−1.61236			−0.806179	−	0.591671i	$-0.798468\pi$
$349$	−30.1213			−1.61236			−0.806179	+	0.591671i	$0.798468\pi$
$350$	11.4309			0.611006
$351$	17.2191	−	7.38264i	0.919086	−	0.394056i
$352$	37.2138			1.98350
$353$	31.4385			1.67330			0.836651	−	0.547736i	$-0.184510\pi$
$353$	31.4385			1.67330			0.836651	+	0.547736i	$0.184510\pi$
$354$	28.1853	+	19.4791i	1.49803	+	1.03530i
$355$	38.6726			2.05253
$356$	−6.04840	+	10.4761i	−0.320565	+	0.555234i
$357$	5.90315	+	4.07971i	0.312428	+	0.215921i
$358$	−10.5656	+	18.3001i	−0.558407	+	0.967190i
$359$	0.224911			0.0118703			0.00593516	−	0.999982i	$-0.498111\pi$
$359$	0.224911			0.0118703			0.00593516	+	0.999982i	$0.498111\pi$
$360$	0.517264	+	0.0846799i	0.0272622	+	0.00446302i
$361$	−18.5721	+	32.1678i	−0.977480	+	1.69304i
$362$	−22.1935			−1.16646
$363$	−14.9318	−	10.3195i	−0.783716	−	0.541632i
$364$	16.2672	−	2.04148i	0.852634	−	0.107003i
$365$	15.3942	−	26.6635i	0.805768	−	1.39563i
$366$	30.0904	−	14.2567i	1.57285	−	0.745209i
$367$	−21.0971			−1.10126			−0.550629	−	0.834750i	$-0.685612\pi$
$367$	−21.0971			−1.10126			−0.550629	+	0.834750i	$0.685612\pi$
$368$	3.73110	+	6.46245i	0.194497	+	0.336879i
$369$	−7.00156	+	8.55506i	−0.364486	+	0.445359i
$370$	−10.0840	−	17.4660i	−0.524243	−	0.908016i
$371$	2.82412	−	4.89152i	0.146621	−	0.253955i
$372$	2.38530	−	1.13014i	0.123672	−	0.0585952i
$373$	−13.1160			−0.679121			−0.339561	−	0.940584i	$-0.610278\pi$
$373$	−13.1160			−0.679121			−0.339561	+	0.940584i	$0.610278\pi$
$374$	8.61292	+	14.9180i	0.445363	+	0.771392i
$375$	9.61300	+	6.64361i	0.496413	+	0.343075i
$376$	−0.213942	−	0.370558i	−0.0110332	−	0.0191101i
$377$	−3.74176	−	4.93799i	−0.192711	−	0.254319i
$378$	16.8126	+	16.2051i	0.864745	+	0.833498i
$379$	1.12198	−	1.94333i	0.0576322	−	0.0998219i	−0.835770	−	0.549080i	$-0.814978\pi$
$379$	1.12198	−	1.94333i	0.0576322	−	0.0998219i	0.893402	+	0.449258i	$0.148312\pi$
$380$	−41.8118			−2.14490
$381$	−28.2259	+	13.3733i	−1.44606	+	0.685135i
$382$	−19.8137	+	34.3183i	−1.01376	+	1.75588i
$383$	−13.2616			−0.677638			−0.338819	−	0.940852i	$-0.610027\pi$
$383$	−13.2616			−0.677638			−0.338819	+	0.940852i	$0.610027\pi$
$384$	−0.725031	−	0.501074i	−0.0369991	−	0.0255703i
$385$	14.2446	+	24.6724i	0.725972	+	1.25742i
$386$	10.7776	+	18.6673i	0.548564	+	0.950141i
$387$	−12.1399	−	1.98738i	−0.617104	−	0.101024i
$388$	−6.23491	+	10.7992i	−0.316530	+	0.548246i
$389$	−1.38426	−	2.39760i	−0.0701845	−	0.121563i	0.828798	−	0.559549i	$-0.189025\pi$
$389$	−1.38426	−	2.39760i	−0.0701845	−	0.121563i	−0.898982	+	0.437985i	$0.855692\pi$
$390$	−30.5501	−	15.9004i	−1.54696	−	0.805147i
$391$	−1.75489	+	3.03955i	−0.0887484	+	0.153717i
$392$	−0.0633236	−	0.109680i	−0.00319833	−	0.00553966i
$393$	−16.6051	+	7.86743i	−0.837618	+	0.396859i
$394$	19.8543	−	34.3887i	1.00025	−	1.73248i
$395$	4.14021			0.208317
$396$	9.98621	+	26.4239i	0.501826	+	1.32785i
$397$	1.66609	+	2.88575i	0.0836185	+	0.144832i	0.904802	−	0.425833i	$-0.140019\pi$
$397$	1.66609	+	2.88575i	0.0836185	+	0.144832i	−0.821183	+	0.570665i	$0.806686\pi$
$398$	9.15712	+	15.8606i	0.459005	+	0.795020i
$399$	−23.8951	−	16.5141i	−1.19625	−	0.826740i
$400$	5.00544	+	8.66967i	0.250272	+	0.433484i
$401$	6.27405	+	10.8670i	0.313311	+	0.542671i	0.979077	−	0.203490i	$-0.0652284\pi$
$401$	6.27405	+	10.8670i	0.313311	+	0.542671i	−0.665766	+	0.746161i	$0.731895\pi$
$402$	3.45479	−	42.4878i	0.172309	−	2.11910i
$403$	−2.68338	+	0.336755i	−0.133668	+	0.0167750i
$404$	−19.1640			−0.953447
$405$	−4.88823	−	24.2310i	−0.242898	−	1.20405i
$406$	3.86099	−	6.68743i	0.191618	−	0.331892i
$407$	8.47443	−	14.6781i	0.420062	−	0.727568i
$408$	0.0165294	−	0.203282i	0.000818327	−	0.0100640i
$409$	3.24471			0.160441			0.0802204	−	0.996777i	$-0.474438\pi$
$409$	3.24471			0.160441			0.0802204	+	0.996777i	$0.474438\pi$
$410$	20.3220			1.00363
$411$	9.30924	−	4.41067i	0.459191	−	0.217562i
$412$	2.70086	−	4.67802i	0.133062	−	0.230470i
$413$	11.0243	−	19.0947i	0.542471	−	0.939587i
$414$	−7.23363	+	8.83862i	−0.355513	+	0.434395i
$415$	−36.1898			−1.77649
$416$	17.4849	+	23.0748i	0.857269	+	1.13133i
$417$	19.6314	+	13.5674i	0.961353	+	0.664398i
$418$	−34.8639	−	60.3861i	−1.70525	−	2.95358i
$419$	−0.112885	−	0.195522i	−0.00551477	−	0.00955187i	0.863255	−	0.504768i	$-0.168422\pi$
$419$	−0.112885	−	0.195522i	−0.00551477	−	0.00955187i	−0.868770	+	0.495216i	$0.835089\pi$
$420$	1.75312	−	21.5603i	0.0855436	−	1.05204i
$421$	9.27429	+	16.0635i	0.452001	+	0.782889i	0.998510	−	0.0545639i	$-0.0173769\pi$
$421$	9.27429	+	16.0635i	0.452001	+	0.782889i	−0.546509	+	0.837453i	$0.684044\pi$
$422$	1.33328	+	2.30931i	0.0649031	+	0.112415i
$423$	−12.7804	+	15.6161i	−0.621403	+	0.759280i
$424$	−0.160538			−0.00779640
$425$	−2.35426	+	4.07769i	−0.114198	+	0.197797i
$426$	3.96865	−	48.8074i	0.192282	−	2.36473i
$427$	−10.7140	−	18.5571i	−0.518485	−	0.898042i
$428$	−0.303929	+	0.526420i	−0.0146910	+	0.0254455i
$429$	−1.26470	−	28.9153i	−0.0610602	−	1.39604i
$430$	11.3068	+	19.5839i	0.545262	+	0.944421i
$431$	−9.27867	+	16.0711i	−0.446938	+	0.774119i	−0.998185	−	0.0602229i	$-0.980819\pi$
$431$	−9.27867	+	16.0711i	−0.446938	+	0.774119i	0.551247	+	0.834342i	$0.314152\pi$
$432$	−4.92860	+	19.8474i	−0.237128	+	0.954907i
$433$	−11.2967	−	19.5665i	−0.542886	−	0.940305i	−0.998737	−	0.0502494i	$-0.983998\pi$
$433$	−11.2967	−	19.5665i	−0.542886	−	0.940305i	0.455851	−	0.890056i	$-0.349335\pi$
$434$	−1.68537	−	2.91915i	−0.0809004	−	0.140124i
$435$	−7.38723	+	3.50003i	−0.354191	+	0.167814i
$436$	1.43889			0.0689101
$437$	7.10354	−	12.3037i	0.339808	−	0.588565i
$438$	−32.0713	−	22.1647i	−1.53243	−	1.05907i
$439$	−31.8232			−1.51884			−0.759419	−	0.650602i	$-0.774516\pi$
$439$	−31.8232			−1.51884			−0.759419	+	0.650602i	$0.774516\pi$
$440$	0.404869	−	0.701254i	0.0193014	−	0.0334310i
$441$	−3.78280	+	4.62213i	−0.180133	+	0.220101i
$442$	−5.20327	+	12.3497i	−0.247494	+	0.587418i
$443$	−5.66525	−	9.81251i	−0.269164	−	0.466206i	0.699482	−	0.714650i	$-0.253414\pi$
$443$	−5.66525	−	9.81251i	−0.269164	−	0.466206i	−0.968646	+	0.248444i	$0.920081\pi$
$444$	−11.6297	+	5.51011i	−0.551923	+	0.261498i
$445$	−8.17666	−	14.1624i	−0.387611	−	0.671362i
$446$	−14.2630			−0.675370
$447$	−15.4092	−	10.6494i	−0.728828	−	0.503699i
$448$	−9.23373	+	15.9933i	−0.436253	+	0.755612i
$449$	−11.0274	−	19.1000i	−0.520416	−	0.901387i	−0.999718	−	0.0237368i	$-0.992444\pi$
$449$	−11.0274	−	19.1000i	−0.520416	−	0.901387i	0.479302	−	0.877650i	$-0.340890\pi$
$450$	−9.70424	+	11.8574i	−0.457462	+	0.558964i
$451$	8.53914	+	14.7902i	0.402092	+	0.696444i
$452$	−17.7731			−0.835976
$453$	−1.81131	+	22.2759i	−0.0851029	+	1.04661i
$454$	−9.84081	+	17.0448i	−0.461852	+	0.799952i
$455$	−8.60551	+	20.4248i	−0.403433	+	0.957531i
$456$	−0.0669087	+	0.822859i	−0.00313329	+	0.0385339i
$457$	35.5514			1.66302			0.831511	−	0.555508i	$-0.187476\pi$
$457$	35.5514			1.66302			0.831511	+	0.555508i	$0.187476\pi$
$458$	−0.283816	+	0.491585i	−0.0132619	+	0.0229702i
$459$	−9.24341	+	2.65995i	−0.431446	+	0.124156i
$460$	10.5803			0.493309
$461$	−15.8589	+	27.4684i	−0.738623	+	1.27933i	0.214493	+	0.976726i	$0.431190\pi$
$461$	−15.8589	+	27.4684i	−0.738623	+	1.27933i	−0.953116	+	0.302607i	$0.902143\pi$
$462$	32.6000	−	15.4457i	1.51669	−	0.718599i
$463$	16.2472	−	28.1409i	0.755070	−	1.30782i	−0.190270	−	0.981732i	$-0.560936\pi$
$463$	16.2472	−	28.1409i	0.755070	−	1.30782i	0.945340	−	0.326087i	$-0.105730\pi$
$464$	6.76272			0.313951
$465$	−0.289188	+	3.55651i	−0.0134108	+	0.164929i
$466$	50.1716			2.32416
$467$	−12.2005			−0.564570			−0.282285	−	0.959331i	$-0.591092\pi$
$467$	−12.2005			−0.564570			−0.282285	+	0.959331i	$0.591092\pi$
$468$	−11.6924	+	18.6073i	−0.540480	+	0.860124i
$469$	−27.4328			−1.26673
$470$	37.0951			1.71107
$471$	13.2324	−	6.26944i	0.609716	−	0.288881i
$472$	−0.626680			−0.0288453
$473$	−9.50202	+	16.4580i	−0.436903	+	0.756739i
$474$	0.424876	−	5.22522i	0.0195152	−	0.240002i
$475$	9.52971	−	16.5060i	0.437253	−	0.757345i
$476$	−8.41708			−0.385796
$477$	2.67651	+	7.08215i	0.122549	+	0.324269i
$478$	−7.74143	+	13.4086i	−0.354085	+	0.613293i
$479$	−29.8958			−1.36597			−0.682987	−	0.730431i	$-0.739319\pi$
$479$	−29.8958			−1.36597			−0.682987	+	0.730431i	$0.739319\pi$
$480$	34.5199	−	16.3554i	1.57561	−	0.746516i
$481$	13.0830	−	1.64188i	0.596535	−	0.0748632i
$482$	−30.2949	+	52.4723i	−1.37989	+	2.39005i
$483$	6.04657	+	4.17883i	0.275129	+	0.190143i
$484$	21.2907			0.967758
$485$	−8.42880	−	14.5991i	−0.382732	−	0.662911i
$486$	−31.0827	+	3.68264i	−1.40994	+	0.167048i
$487$	−4.97497	−	8.61690i	−0.225437	−	0.390469i	0.731013	−	0.682363i	$-0.239048\pi$
$487$	−4.97497	−	8.61690i	−0.225437	−	0.390469i	−0.956451	+	0.291894i	$0.905714\pi$
$488$	−0.304519	+	0.527442i	−0.0137849	+	0.0238762i
$489$	3.37578	−	41.5161i	0.152658	−	1.87742i
$490$	10.9796			0.496008
$491$	−1.87632	−	3.24988i	−0.0846771	−	0.146665i	0.820576	−	0.571537i	$-0.193653\pi$
$491$	−1.87632	−	3.24988i	−0.0846771	−	0.146665i	−0.905254	+	0.424872i	$0.860319\pi$
$492$	1.05094	−	12.9247i	0.0473798	−	0.582688i
$493$	1.59039	+	2.75463i	0.0716275	+	0.124062i
$494$	21.0621	−	49.9901i	0.947630	−	2.24916i
$495$	−37.6860	−	6.16947i	−1.69386	−	0.277297i
$496$	1.47601	−	2.55652i	0.0662746	−	0.114791i
$497$	−31.5132			−1.41356
$498$	−3.71386	+	45.6739i	−0.166422	+	2.04670i
$499$	14.0065	−	24.2599i	0.627015	−	1.08602i	−0.361132	−	0.932515i	$-0.617610\pi$
$499$	14.0065	−	24.2599i	0.627015	−	1.08602i	0.988147	−	0.153507i	$-0.0490569\pi$
$500$	−13.7068			−0.612987
$501$	−1.33534	+	16.4224i	−0.0596588	+	0.733698i
$502$	3.89549	+	6.74718i	0.173864	+	0.301141i
$503$	−7.62622	−	13.2090i	−0.340037	−	0.588961i	0.644403	−	0.764686i	$-0.277106\pi$
$503$	−7.62622	−	13.2090i	−0.340037	−	0.588961i	−0.984439	+	0.175726i	$0.943773\pi$
$504$	−0.421503	−	0.0690032i	−0.0187752	−	0.00307364i
$505$	12.9537	−	22.4364i	0.576430	−	0.998406i
$506$	8.82218	+	15.2805i	0.392194	+	0.679299i
$507$	17.3350	−	14.3700i	0.769874	−	0.638196i
$508$	18.3185	−	31.7285i	0.812750	−	1.40772i
$509$	6.90107	+	11.9530i	0.305885	+	0.529808i	0.977458	−	0.211130i	$-0.0677145\pi$
$509$	6.90107	+	11.9530i	0.305885	+	0.529808i	−0.671573	+	0.740938i	$0.734381\pi$
$510$	14.5458	+	10.0527i	0.644100	+	0.445142i
$511$	−12.5443	+	21.7273i	−0.554926	+	0.961159i
$512$	−32.1023			−1.41873
$513$	37.4161	−	10.7671i	1.65196	−	0.475380i
$514$	−7.70943	−	13.3531i	−0.340048	−	0.588981i
$515$	3.65121	+	6.32408i	0.160891	+	0.278672i
$516$	13.0399	−	6.17826i	0.574051	−	0.271983i
$517$	15.5870	+	26.9975i	0.685517	+	1.18735i
$518$	8.21717	+	14.2326i	0.361042	+	0.625342i
$519$	−17.9514	+	8.50529i	−0.787980	+	0.373341i
$520$	0.625047	−	0.0784413i	0.0274101	−	0.00343988i
$521$	19.0802			0.835917			0.417959	−	0.908466i	$-0.362746\pi$
$521$	19.0802			0.835917			0.417959	+	0.908466i	$0.362746\pi$
$522$	3.65918	+	9.68235i	0.160158	+	0.423785i
$523$	−4.58164	+	7.93564i	−0.200341	+	0.347001i	−0.948638	−	0.316362i	$-0.897538\pi$
$523$	−4.58164	+	7.93564i	−0.200341	+	0.347001i	0.748297	+	0.663364i	$0.230872\pi$
$524$	10.7766	−	18.6657i	0.470780	−	0.815414i
$525$	8.11175	+	5.60609i	0.354026	+	0.244670i
$526$	20.0061			0.872307
$527$	1.38845			0.0604818
$528$	25.9898	+	17.9617i	1.13106	+	0.781685i
$529$	9.70248	−	16.8052i	0.421847	−	0.730660i
$530$	6.95885	−	12.0531i	0.302273	−	0.523553i
$531$	10.4481	+	27.6461i	0.453408	+	1.19974i
$532$	34.0712			1.47717
$533$	−5.15870	+	12.2440i	−0.223448	+	0.530345i
$534$	−18.7130	+	8.86611i	−0.809789	+	0.383674i
$535$	−0.410873	−	0.711653i	−0.0177636	−	0.0307674i
$536$	0.389857	+	0.675251i	0.0168392	+	0.0291664i
$537$	−16.4727	+	7.80467i	−0.710848	+	0.336796i
$538$	4.91254	+	8.50877i	0.211795	+	0.366839i
$539$	4.61353	+	7.99086i	0.198719	+	0.344191i
$540$	20.8765	+	20.1222i	0.898382	+	0.865920i
$541$	3.43119			0.147518			0.0737592	−	0.997276i	$-0.476500\pi$
$541$	3.43119			0.147518			0.0737592	+	0.997276i	$0.476500\pi$
$542$	−5.31957	+	9.21376i	−0.228495	+	0.395765i
$543$	−15.7492	−	10.8844i	−0.675865	−	0.467095i
$544$	−7.43174	−	12.8722i	−0.318633	−	0.551889i
$545$	−0.972594	+	1.68458i	−0.0416613	+	0.0721595i
$546$	24.8944	+	12.9567i	1.06538	+	0.554498i
$547$	3.91240	+	6.77648i	0.167282	+	0.289741i	0.937463	−	0.348084i	$-0.113168\pi$
$547$	3.91240	+	6.77648i	0.167282	+	0.289741i	−0.770181	+	0.637825i	$0.779834\pi$
$548$	−6.04165	+	10.4644i	−0.258086	+	0.447019i
$549$	28.3452	+	4.64031i	1.20974	+	0.198044i
$550$	11.8353	+	20.4994i	0.504661	+	0.874098i
$551$	−6.43767	−	11.1504i	−0.274254	−	0.475022i
$552$	0.0169310	−	0.208221i	0.000720631	−	0.00886248i
$553$	−3.37374			−0.143466
$554$	2.68772	−	4.65526i	0.114190	−	0.197783i
$555$	1.40996	−	17.3400i	0.0598496	−	0.736044i
$556$	−27.9917			−1.18711
$557$	2.92973	−	5.07443i	0.124136	−	0.215011i	−0.797259	−	0.603638i	$-0.793717\pi$
$557$	2.92973	−	5.07443i	0.124136	−	0.215011i	0.921395	+	0.388627i	$0.127051\pi$
$558$	4.45887	+	0.729949i	0.188759	+	0.0309012i
$559$	−14.6694	+	1.84097i	−0.620452	+	0.0778647i
$560$	−12.0964	−	20.9515i	−0.511165	−	0.885363i
$561$	−1.20427	+	14.8104i	−0.0508443	+	0.625296i
$562$	2.23513	+	3.87136i	0.0942833	+	0.163304i
$563$	−31.7218			−1.33692			−0.668458	−	0.743750i	$-0.733045\pi$
$563$	−31.7218			−1.33692			−0.668458	+	0.743750i	$0.733045\pi$
$564$	1.91834	−	23.5922i	0.0807766	−	0.993410i
$565$	12.0135	−	20.8079i	0.505410	−	0.875396i
$566$	−2.57762	−	4.46457i	−0.108345	−	0.187660i
$567$	3.98327	+	19.7451i	0.167282	+	0.829217i
$568$	0.447843	+	0.775688i	0.0187911	+	0.0325471i
$569$	7.47156			0.313224			0.156612	−	0.987660i	$-0.449943\pi$
$569$	7.47156			0.313224			0.156612	+	0.987660i	$0.449943\pi$
$570$	−58.8795	−	40.6921i	−2.46619	−	1.70440i
$571$	−7.92734	+	13.7306i	−0.331749	+	0.574606i	−0.982855	−	0.184381i	$-0.940972\pi$
$571$	−7.92734	+	13.7306i	−0.331749	+	0.574606i	0.651106	+	0.758987i	$0.274305\pi$
$572$	20.5039	+	27.0589i	0.857310	+	1.13139i
$573$	−30.8914	+	14.6362i	−1.29050	+	0.611435i
$574$	−16.5598			−0.691194
$575$	−2.41146	+	4.17677i	−0.100565	+	0.174183i
$576$	−8.75110	−	23.1558i	−0.364629	−	0.964824i
$577$	41.9148			1.74494			0.872468	−	0.488671i	$-0.162518\pi$
$577$	41.9148			1.74494			0.872468	+	0.488671i	$0.162518\pi$
$578$	−13.6271	+	23.6029i	−0.566814	+	0.981750i
$579$	−1.50694	+	18.5326i	−0.0626261	+	0.770191i
$580$	4.79427	−	8.30392i	0.199071	−	0.344802i
$581$	29.4900			1.22345
$582$	−19.2900	+	9.13951i	−0.799597	+	0.378845i
$583$	11.6962			0.484407
$584$	0.713081			0.0295075
$585$	−13.8813	−	26.2663i	−0.573922	−	1.08598i
$586$	2.81231			0.116175
$587$	−30.2480			−1.24847			−0.624234	−	0.781238i	$-0.714589\pi$
$587$	−30.2480			−1.24847			−0.624234	+	0.781238i	$0.714589\pi$
$588$	0.567800	−	6.98293i	0.0234157	−	0.287971i
$589$	−5.62025			−0.231578
$590$	27.1648	−	47.0508i	1.11836	−	1.93705i
$591$	30.9547	−	14.6662i	1.27331	−	0.603286i
$592$	−7.19639	+	12.4645i	−0.295770	+	0.512288i
$593$	24.2910			0.997513			0.498757	−	0.866742i	$-0.333790\pi$
$593$	24.2910			0.997513			0.498757	+	0.866742i	$0.333790\pi$
$594$	−11.6537	+	46.9290i	−0.478156	+	1.92552i
$595$	5.68940	−	9.85433i	0.233243	−	0.403988i
$596$	21.9713			0.899981
$597$	−1.28036	+	15.7462i	−0.0524017	+	0.644449i
$598$	−5.32969	+	12.6498i	−0.217947	+	0.517289i
$599$	−7.73002	+	13.3888i	−0.315840	+	0.547051i	−0.979616	−	0.200881i	$-0.935620\pi$
$599$	−7.73002	+	13.3888i	−0.315840	+	0.547051i	0.663776	+	0.747932i	$0.268953\pi$
$600$	0.0227137	−	0.279338i	0.000927282	−	0.0114039i
$601$	−17.6849			−0.721381			−0.360690	−	0.932686i	$-0.617459\pi$
$601$	−17.6849			−0.721381			−0.360690	+	0.932686i	$0.617459\pi$
$602$	−9.21357	−	15.9584i	−0.375517	−	0.650414i
$603$	23.2891	−	28.4565i	0.948405	−	1.15884i
$604$	−13.1079	−	22.7035i	−0.533351	−	0.923792i
$605$	−14.3911	+	24.9262i	−0.585083	+	1.01339i
$606$	−26.9869	−	18.6508i	−1.09627	−	0.757638i
$607$	−14.6193			−0.593378			−0.296689	−	0.954974i	$-0.595882\pi$
$607$	−14.6193			−0.593378			−0.296689	+	0.954974i	$0.595882\pi$
$608$	30.0827	+	52.1047i	1.22001	+	2.11313i
$609$	6.01963	−	2.85207i	0.243928	−	0.115572i
$610$	−26.4000	−	45.7262i	−1.06891	−	1.85140i
$611$	−9.41650	+	22.3497i	−0.380951	+	0.904171i
$612$	7.14567	−	8.73115i	0.288847	−	0.352936i
$613$	−18.1516	+	31.4395i	−0.733135	+	1.26983i	0.222401	+	0.974955i	$0.428610\pi$
$613$	−18.1516	+	31.4395i	−0.733135	+	1.26983i	−0.955537	+	0.294872i	$0.904723\pi$
$614$	36.6913			1.48074
$615$	14.4212	+	9.96662i	0.581520	+	0.401893i
$616$	−0.329916	+	0.571431i	−0.0132927	+	0.0230236i
$617$	−21.9483			−0.883606			−0.441803	−	0.897112i	$-0.645661\pi$
$617$	−21.9483			−0.883606			−0.441803	+	0.897112i	$0.645661\pi$
$618$	8.35610	−	3.95908i	0.336132	−	0.159257i
$619$	6.99888	+	12.1224i	0.281309	+	0.487241i	0.971707	−	0.236188i	$-0.0758982\pi$
$619$	6.99888	+	12.1224i	0.281309	+	0.487241i	−0.690399	+	0.723429i	$0.742565\pi$
$620$	−2.09276	−	3.62477i	−0.0840473	−	0.145574i
$621$	−9.46799	+	2.72458i	−0.379937	+	0.109334i
$622$	6.31717	−	10.9417i	0.253296	−	0.438721i
$623$	6.66292	+	11.5405i	0.266944	+	0.462361i
$624$	1.07397	+	24.5546i	0.0429931	+	0.982969i
$625$	15.6240	−	27.0616i	0.624962	−	1.08247i
$626$	−21.1937	−	36.7086i	−0.847071	−	1.46717i
$627$	4.87472	−	59.9505i	0.194678	−	2.39419i
$628$	−8.58775	+	14.8744i	−0.342688	+	0.593554i
$629$	−6.76950			−0.269918
$630$	23.4517	−	28.6551i	0.934337	−	1.14165i
$631$	−16.6485	−	28.8360i	−0.662765	−	1.14794i	−0.979886	−	0.199557i	$-0.936050\pi$
$631$	−16.6485	−	28.8360i	−0.662765	−	1.14794i	0.317121	−	0.948385i	$-0.397284\pi$
$632$	0.0479452	+	0.0830435i	0.00190716	+	0.00330329i
$633$	−0.186421	+	2.29265i	−0.00740958	+	0.0911247i
$634$	9.55171	+	16.5440i	0.379347	+	0.657048i
$635$	24.7642	+	42.8928i	0.982737	+	1.70215i
$636$	−7.30579	−	5.04909i	−0.289693	−	0.200209i
$637$	−2.78714	+	6.61517i	−0.110431	+	0.262103i
$638$	15.9904			0.633067
$639$	26.7531	−	32.6891i	1.05834	−	1.29316i
$640$	−0.698778	+	1.21032i	−0.0276216	+	0.0478421i
$641$	−0.998924	+	1.73019i	−0.0394551	+	0.0683383i	−0.885079	−	0.465442i	$-0.845896\pi$
$641$	−0.998924	+	1.73019i	−0.0394551	+	0.0683383i	0.845624	+	0.533780i	$0.179229\pi$
$642$	−0.940317	+	0.445517i	−0.0371113	+	0.0175832i
$643$	18.4129			0.726135			0.363067	−	0.931763i	$-0.381729\pi$
$643$	18.4129			0.726135			0.363067	+	0.931763i	$0.381729\pi$
$644$	−8.62158			−0.339738
$645$	−1.58093	+	19.4427i	−0.0622491	+	0.765554i
$646$	−13.9249	+	24.1186i	−0.547868	+	0.948935i
$647$	20.0900	−	34.7969i	0.789820	−	1.36801i	−0.136257	−	0.990674i	$-0.543507\pi$
$647$	20.0900	−	34.7969i	0.789820	−	1.36801i	0.926077	−	0.377335i	$-0.123159\pi$
$648$	0.429413	−	0.378651i	0.0168689	−	0.0148748i
$649$	45.6576			1.79222
$650$	−7.15002	+	16.9703i	−0.280447	+	0.665629i
$651$	0.235651	−	2.89809i	0.00923589	−	0.113585i
$652$	24.4294	+	42.3129i	0.956729	+	1.65710i
$653$	−16.0654	−	27.8261i	−0.628689	−	1.08892i	−0.987815	−	0.155632i	$-0.950259\pi$
$653$	−16.0654	−	27.8261i	−0.628689	−	1.08892i	0.359127	−	0.933289i	$-0.383075\pi$
$654$	2.02624	+	1.40035i	0.0792324	+	0.0547581i
$655$	14.5686	+	25.2336i	0.569243	+	0.985958i
$656$	−7.25134	−	12.5597i	−0.283117	−	0.490374i
$657$	−11.8886	−	31.4577i	−0.463818	−	1.22728i
$658$	−30.2277			−1.17840
$659$	7.67662	−	13.2963i	0.299039	−	0.517950i	−0.676878	−	0.736096i	$-0.736667\pi$
$659$	7.67662	−	13.2963i	0.299039	−	0.517950i	0.975916	+	0.218145i	$0.0700007\pi$
$660$	40.4801	−	19.1793i	1.57568	−	0.746552i
$661$	9.62715	+	16.6747i	0.374453	+	0.648571i	0.990245	−	0.139337i	$-0.0444972\pi$
$661$	9.62715	+	16.6747i	0.374453	+	0.648571i	−0.615792	+	0.787909i	$0.711164\pi$
$662$	6.28435	−	10.8848i	0.244248	−	0.423050i
$663$	−9.74915	+	6.21195i	−0.378626	+	0.241252i
$664$	−0.419091	−	0.725887i	−0.0162639	−	0.0281699i
$665$	−23.0299	+	39.8890i	−0.893062	+	1.54683i
$666$	−21.7396	−	3.55893i	−0.842392	−	0.137906i
$667$	1.62903	+	2.82156i	0.0630762	+	0.109251i
$668$	−9.66345	−	16.7376i	−0.373890	−	0.647596i
$669$	−10.1215	−	6.99503i	−0.391319	−	0.270444i
$670$	−67.5967			−2.61149
$671$	22.1861	−	38.4275i	0.856486	−	1.48348i
$672$	−28.1292	+	13.3275i	−1.08511	+	0.514119i
$673$	17.6532			0.680483			0.340241	−	0.940338i	$-0.389491\pi$
$673$	17.6532			0.680483			0.340241	+	0.940338i	$0.389491\pi$
$674$	−6.20870	+	10.7538i	−0.239150	+	0.414220i
$675$	−12.7017	+	3.65515i	−0.488890	+	0.140687i
$676$	−7.14436	+	25.4272i	−0.274783	+	0.977970i
$677$	−0.157510	−	0.272815i	−0.00605359	−	0.0104851i	0.862983	−	0.505233i	$-0.168594\pi$
$677$	−0.157510	−	0.272815i	−0.00605359	−	0.0104851i	−0.869036	+	0.494748i	$0.835260\pi$
$678$	−25.0281	−	17.2971i	−0.961199	−	0.664292i
$679$	6.86838	+	11.8964i	0.263584	+	0.456541i
$680$	−0.323415			−0.0124024
$681$	−15.3427	+	7.26931i	−0.587934	+	0.278560i
$682$	3.49001	−	6.04488i	0.133639	−	0.231470i
$683$	22.2504	+	38.5388i	0.851388	+	1.47465i	0.879956	+	0.475056i	$0.157572\pi$
$683$	22.2504	+	38.5388i	0.851388	+	1.47465i	−0.0285673	+	0.999592i	$0.509094\pi$
$684$	−28.9247	+	35.3425i	−1.10596	+	1.35136i
$685$	−8.16753	−	14.1466i	−0.312065	−	0.540513i
$686$	−40.4042			−1.54264
$687$	−0.442496	+	0.209652i	−0.0168823	+	0.00799873i
$688$	8.06901	−	13.9759i	0.307628	−	0.532827i
$689$	5.49545	+	7.25233i	0.209360	+	0.276292i
$690$	14.8992	+	10.2970i	0.567204	+	0.391999i
$691$	−1.68374			−0.0640526			−0.0320263	−	0.999487i	$-0.510196\pi$
$691$	−1.68374			−0.0640526			−0.0320263	+	0.999487i	$0.510196\pi$
$692$	11.6504	−	20.1790i	0.442881	−	0.767092i
$693$	30.7092	+	5.02732i	1.16654	+	0.190972i
$694$	−14.8265			−0.562805
$695$	18.9206	−	32.7714i	0.717698	−	1.24309i
$696$	−0.155750	−	0.107640i	−0.00590368	−	0.00408008i
$697$	3.41060	−	5.90733i	0.129186	−	0.223756i
$698$	60.4808			2.28923
$699$	35.6035	+	24.6059i	1.34665	+	0.930679i
$700$	−11.5662			−0.437163
$701$	42.4593			1.60367			0.801833	−	0.597548i	$-0.203858\pi$
$701$	42.4593			1.60367			0.801833	+	0.597548i	$0.203858\pi$
$702$	−34.5743	+	14.8236i	−1.30492	+	0.559482i
$703$	27.4020			1.03349
$704$	−38.2418			−1.44129
$705$	26.3240	+	18.1927i	0.991418	+	0.685177i
$706$	−63.1255			−2.37576
$707$	−10.5556	+	18.2828i	−0.396982	+	0.687594i
$708$	−28.5191	−	19.7098i	−1.07181	−	0.740738i
$709$	11.2892	−	19.5535i	0.423975	−	0.734346i	−0.572349	−	0.820010i	$-0.693968\pi$
$709$	11.2892	−	19.5535i	0.423975	−	0.734346i	0.996324	+	0.0856638i	$0.0273011\pi$
$710$	−77.6510			−2.91419
$711$	2.86413	−	3.49962i	0.107413	−	0.131246i
$712$	0.189377	−	0.328011i	0.00709722	−	0.0122927i
$713$	1.42218			0.0532611
$714$	−11.8530	−	8.19167i	−0.443586	−	0.306565i
$715$	−45.5386	+	5.71495i	−1.70305	+	0.213727i
$716$	10.6907	−	18.5168i	0.399529	−	0.692005i
$717$	−12.0696	+	5.71852i	−0.450747	+	0.213562i
$718$	−0.451599			−0.0168535
$719$	26.4085	+	45.7408i	0.984870	+	1.70584i	0.642514	+	0.766274i	$0.277891\pi$
$719$	26.4085	+	45.7408i	0.984870	+	1.70584i	0.342355	+	0.939571i	$0.388775\pi$
$720$	32.0025	+	5.23904i	1.19266	+	0.195248i
$721$	−2.97526	−	5.15330i	−0.110805	−	0.191919i
$722$	37.2910	−	64.5900i	1.38783	−	2.40379i
$723$	−47.2325	+	22.3785i	−1.75659	+	0.832266i
$724$	22.4563			0.834580
$725$	2.18541	+	3.78525i	0.0811642	+	0.140581i
$726$	29.9816	+	20.7205i	1.11272	+	0.769010i
$727$	−11.2248	−	19.4420i	−0.416306	−	0.721063i	0.579258	−	0.815144i	$-0.303342\pi$
$727$	−11.2248	−	19.4420i	−0.416306	−	0.721063i	−0.995565	+	0.0940806i	$0.970009\pi$
$728$	−0.509332	+	0.0639195i	−0.0188771	+	0.00236901i
$729$	−23.8635	−	12.6307i	−0.883832	−	0.467804i
$730$	−30.9101	+	53.5378i	−1.14403	+	1.98152i
$731$	7.59035			0.280739
$732$	−30.4467	+	14.4255i	−1.12534	+	0.533182i
$733$	−13.3860	+	23.1852i	−0.494423	+	0.856366i	−0.999979	−	0.00642752i	$-0.997954\pi$
$733$	−13.3860	+	23.1852i	−0.494423	+	0.856366i	0.505556	+	0.862794i	$0.331287\pi$
$734$	42.3609			1.56357
$735$	7.79150	+	5.38476i	0.287394	+	0.198620i
$736$	−7.61230	−	13.1849i	−0.280593	−	0.486002i
$737$	−28.4035	−	49.1963i	−1.04626	−	1.81217i
$738$	14.0585	−	17.1777i	0.517499	−	0.632322i
$739$	2.79957	−	4.84900i	0.102984	−	0.178373i	−0.809929	−	0.586528i	$-0.800494\pi$
$739$	2.79957	−	4.84900i	0.102984	−	0.178373i	0.912913	+	0.408155i	$0.133828\pi$
$740$	10.2034	+	17.6729i	0.375086	+	0.649667i
$741$	39.4632	−	25.1451i	1.44972	−	0.923729i
$742$	−5.67056	+	9.82170i	−0.208173	+	0.360566i
$743$	−15.4393	−	26.7416i	−0.566412	−	0.981054i	−0.996917	−	0.0784655i	$-0.974998\pi$
$743$	−15.4393	−	26.7416i	−0.566412	−	0.981054i	0.430505	−	0.902588i	$-0.358335\pi$
$744$	−0.0746846	+	0.0353852i	−0.00273807	+	0.00129728i
$745$	−14.8512	+	25.7231i	−0.544106	+	0.942420i
$746$	26.3357			0.964218
$747$	−25.0355	+	30.5904i	−0.916001	+	1.11924i
$748$	−8.71491	−	15.0947i	−0.318649	−	0.551915i
$749$	0.334808	+	0.579904i	0.0122336	+	0.0211892i
$750$	−19.3020	−	13.3397i	−0.704809	−	0.487099i
$751$	5.47437	+	9.48189i	0.199763	+	0.345999i	0.948451	−	0.316923i	$-0.102650\pi$
$751$	5.47437	+	9.48189i	0.199763	+	0.345999i	−0.748689	+	0.662922i	$0.769316\pi$
$752$	−13.2363	−	22.9260i	−0.482679	−	0.836025i
$753$	−0.544673	+	6.69851i	−0.0198490	+	0.244107i
$754$	7.51310	+	9.91501i	0.273611	+	0.361083i
$755$	35.4403			1.28980
$756$	−17.0116	−	16.3969i	−0.618708	−	0.596351i
$757$	5.98592	−	10.3679i	0.217562	−	0.376828i	−0.736500	−	0.676437i	$-0.763523\pi$
$757$	5.98592	−	10.3679i	0.217562	−	0.376828i	0.954062	+	0.299609i	$0.0968563\pi$
$758$	−2.25283	+	3.90201i	−0.0818264	+	0.141727i
$759$	−1.23353	+	15.1702i	−0.0447743	+	0.550645i
$760$	1.30914			0.0474875
$761$	−40.3848			−1.46395			−0.731973	−	0.681334i	$-0.761400\pi$
$761$	−40.3848			−1.46395			−0.731973	+	0.681334i	$0.761400\pi$
$762$	56.6749	−	26.8523i	2.05312	−	0.972756i
$763$	0.792538	−	1.37272i	0.0286918	−	0.0496956i
$764$	20.0483	−	34.7247i	0.725323	−	1.25630i
$765$	5.39203	+	14.2675i	0.194949	+	0.515843i
$766$	26.6281			0.962113
$767$	21.4522	+	28.3104i	0.774595	+	1.02223i
$768$	−22.0587	−	15.2449i	−0.795976	−	0.550105i
$769$	−0.835182	−	1.44658i	−0.0301174	−	0.0521649i	0.850574	−	0.525856i	$-0.176255\pi$
$769$	−0.835182	−	1.44658i	−0.0301174	−	0.0521649i	−0.880691	+	0.473691i	$0.842921\pi$
$770$	−28.6018	−	49.5398i	−1.03074	−	1.78529i
$771$	1.07794	−	13.2568i	0.0388212	−	0.477432i
$772$	−10.9052	−	18.8883i	−0.392486	−	0.679807i
$773$	−7.19915	−	12.4693i	−0.258935	−	0.448489i	0.707022	−	0.707192i	$-0.250038\pi$
$773$	−7.19915	−	12.4693i	−0.258935	−	0.448489i	−0.965957	+	0.258703i	$0.916705\pi$
$774$	24.3757	+	3.99048i	0.876166	+	0.143435i
$775$	1.90792			0.0685346
$776$	0.195217	−	0.338126i	0.00700789	−	0.0121380i
$777$	−1.14894	+	14.1299i	−0.0412179	+	0.506907i
$778$	2.77945	+	4.81415i	0.0996482	+	0.172596i
$779$	−13.8056	+	23.9121i	−0.494638	+	0.856738i
$780$	30.9118	+	16.0887i	1.10682	+	0.576067i
$781$	−32.6282	−	56.5137i	−1.16753	−	2.02222i
$782$	3.52364	−	6.10313i	0.126005	−	0.218247i
$783$	−2.15187	+	8.66552i	−0.0769015	+	0.309680i
$784$	−3.91776	−	6.78575i	−0.139920	−	0.242348i
$785$	−11.6095	−	20.1083i	−0.414362	−	0.717696i
$786$	33.3415	−	15.7970i	1.18925	−	0.563462i
$787$	44.2561			1.57756			0.788780	−	0.614676i	$-0.210713\pi$
$787$	44.2561			1.57756			0.788780	+	0.614676i	$0.210713\pi$
$788$	−20.0894	+	34.7959i	−0.715656	+	1.23955i
$789$	14.1970	+	9.81166i	0.505427	+	0.349304i
$790$	−8.31315			−0.295769
$791$	−9.78941	+	16.9558i	−0.348071	+	0.602877i
$792$	−0.312671	−	0.827342i	−0.0111103	−	0.0293983i
$793$	34.2515	−	4.29845i	1.21631	−	0.152642i
$794$	−3.34534	−	5.79431i	−0.118722	−	0.205632i
$795$	10.8495	−	5.14043i	0.384791	−	0.182312i
$796$	−9.26556	−	16.0484i	−0.328409	−	0.568821i
$797$	36.1661			1.28107			0.640534	−	0.767930i	$-0.278713\pi$
$797$	36.1661			1.28107			0.640534	+	0.767930i	$0.278713\pi$
$798$	47.9792	+	33.1588i	1.69844	+	1.17381i
$799$	6.22558	−	10.7830i	0.220245	−	0.381476i
$800$	−10.2122	−	17.6881i	−0.361058	−	0.625370i
$801$	−17.6276	−	2.88577i	−0.622841	−	0.101964i
$802$	−12.5977	−	21.8198i	−0.444840	−	0.770485i
$803$	−51.9525			−1.83336
$804$	−3.49570	+	42.9909i	−0.123284	+	1.51617i
$805$	5.82763	−	10.0938i	0.205397	−	0.355758i
$806$	5.38796	−	0.676172i	0.189783	−	0.0238171i
$807$	−0.686879	+	8.44739i	−0.0241793	+	0.297362i
$808$	0.600033			0.0211091
$809$	3.76809	−	6.52653i	0.132479	−	0.229460i	−0.792153	−	0.610323i	$-0.791040\pi$
$809$	3.76809	−	6.52653i	0.132479	−	0.229460i	0.924632	+	0.380863i	$0.124373\pi$
$810$	9.81509	+	48.6535i	0.344867	+	1.70951i
$811$	−13.1953			−0.463350			−0.231675	−	0.972793i	$-0.574421\pi$
$811$	−13.1953			−0.463350			−0.231675	+	0.972793i	$0.574421\pi$
$812$	−3.90671	+	6.76662i	−0.137099	+	0.237462i
$813$	−8.29369	+	3.92951i	−0.290872	+	0.137814i
$814$	−17.0158	+	29.4723i	−0.596405	+	1.03300i
$815$	−66.0508			−2.31366
$816$	1.02265	−	12.5768i	0.0358000	−	0.440277i
$817$	−30.7247			−1.07492
$818$	−6.51508			−0.227794
$819$	11.3115	+	21.4036i	0.395255	+	0.747902i
$820$	−20.5627			−0.718080
$821$	−5.52953			−0.192982			−0.0964910	−	0.995334i	$-0.530762\pi$
$821$	−5.52953			−0.192982			−0.0964910	+	0.995334i	$0.530762\pi$
$822$	−18.6921	+	8.85621i	−0.651961	+	0.308896i
$823$	19.4612			0.678374			0.339187	−	0.940719i	$-0.389848\pi$
$823$	19.4612			0.678374			0.339187	+	0.940719i	$0.389848\pi$
$824$	−0.0845647	+	0.146470i	−0.00294595	+	0.00510254i
$825$	−1.65484	+	20.3515i	−0.0576140	+	0.708550i
$826$	−22.1358	+	38.3403i	−0.770202	+	1.33403i
$827$	34.5038			1.19981			0.599907	−	0.800070i	$-0.295204\pi$
$827$	34.5038			1.19981			0.599907	+	0.800070i	$0.295204\pi$
$828$	7.31928	−	8.94329i	0.254363	−	0.310801i
$829$	−23.1955	+	40.1757i	−0.805612	+	1.39536i	0.110265	+	0.993902i	$0.464830\pi$
$829$	−23.1955	+	40.1757i	−0.805612	+	1.39536i	−0.915877	+	0.401459i	$0.868503\pi$
$830$	72.6656			2.52226
$831$	4.19040	−	1.98539i	0.145363	−	0.0688724i
$832$	−17.9679	−	23.7122i	−0.622926	−	0.822073i
$833$	1.84268	−	3.19161i	0.0638450	−	0.110583i
$834$	−39.4180	−	27.2420i	−1.36493	−	0.943315i
$835$	26.1275			0.904178
$836$	35.2768	+	61.1011i	1.22007	+	2.11323i
$837$	2.80617	+	2.70478i	0.0969956	+	0.0934907i
$838$	0.226661	+	0.392589i	0.00782989	+	0.0135618i
$839$	17.2455	−	29.8700i	0.595380	−	1.03123i	−0.398113	−	0.917336i	$-0.630335\pi$
$839$	17.2455	−	29.8700i	0.595380	−	1.03123i	0.993493	−	0.113892i	$-0.0363317\pi$
$840$	−0.0548909	+	0.675061i	−0.00189391	+	0.0232918i
$841$	−26.0473			−0.898184
$842$	−18.6219	−	32.2541i	−0.641753	−	1.11155i
$843$	−0.312519	+	3.84344i	−0.0107637	+	0.132375i
$844$	−1.34907	−	2.33666i	−0.0464369	−	0.0804310i
$845$	−24.9399	−	25.5515i	−0.857959	−	0.878997i
$846$	25.6618	−	31.3556i	0.882270	−	1.07803i
$847$	11.7269	−	20.3116i	0.402941	−	0.697914i
$848$	−9.93227			−0.341076
$849$	0.360407	−	4.43236i	0.0123691	−	0.152118i
$850$	4.72712	−	8.18762i	0.162139	−	0.280833i
$851$	−6.93397			−0.237693
$852$	−4.01565	+	49.3854i	−0.137574	+	1.69191i
$853$	−17.5778	−	30.4457i	−0.601854	−	1.04244i	−0.992540	−	0.121918i	$-0.961096\pi$
$853$	−17.5778	−	30.4457i	−0.601854	−	1.04244i	0.390686	−	0.920524i	$-0.372238\pi$
$854$	21.5126	+	37.2609i	0.736146	+	1.27504i
$855$	−21.8262	−	57.7530i	−0.746440	−	1.97511i
$856$	0.00951612	−	0.0164824i	0.000325254	−	0.000563357i
$857$	−9.80605	−	16.9846i	−0.334968	−	0.580182i	0.648510	−	0.761206i	$-0.275392\pi$
$857$	−9.80605	−	16.9846i	−0.334968	−	0.580182i	−0.983479	+	0.181024i	$0.942059\pi$
$858$	2.53939	+	58.0592i	0.0866934	+	1.98211i
$859$	−9.49035	+	16.4378i	−0.323807	+	0.560849i	−0.981270	−	0.192637i	$-0.938296\pi$
$859$	−9.49035	+	16.4378i	−0.323807	+	0.560849i	0.657464	+	0.753486i	$0.271629\pi$
$860$	−11.4407	−	19.8158i	−0.390124	−	0.675714i
$861$	−11.7514	−	8.12150i	−0.400488	−	0.276780i
$862$	18.6307	−	32.2693i	0.634564	−	1.09910i
$863$	−27.8697			−0.948694			−0.474347	−	0.880338i	$-0.657316\pi$
$863$	−27.8697			−0.948694			−0.474347	+	0.880338i	$0.657316\pi$
$864$	10.0555	−	40.4932i	0.342095	−	1.37761i
$865$	15.7498	+	27.2794i	0.535509	+	0.927529i
$866$	22.6827	+	39.2876i	0.770791	+	1.33505i
$867$	−21.2459	+	10.0662i	−0.721549	+	0.341867i
$868$	1.70533	+	2.95371i	0.0578826	+	0.100256i
$869$	−3.49311	−	6.05025i	−0.118496	−	0.205241i
$870$	14.8329	−	7.02773i	0.502881	−	0.238262i
$871$	17.1592	−	40.7268i	0.581419	−	1.37997i
$872$	−0.0450520			−0.00152565
$873$	−18.1712	−	2.97476i	−0.615001	−	0.100680i
$874$	−14.2632	+	24.7046i	−0.482461	+	0.835647i
$875$	−7.54971	+	13.0765i	−0.255227	+	0.442066i
$876$	32.4511	+	22.4272i	1.09642	+	0.757745i
$877$	11.8206			0.399154			0.199577	−	0.979882i	$-0.436043\pi$
$877$	11.8206			0.399154			0.199577	+	0.979882i	$0.436043\pi$
$878$	63.8979			2.15645
$879$	1.99571	+	1.37925i	0.0673137	+	0.0465210i
$880$	25.0487	−	43.3857i	0.844393	−	1.46253i
$881$	−26.5198	+	45.9336i	−0.893475	+	1.54754i	−0.0577934	+	0.998329i	$0.518406\pi$
$881$	−26.5198	+	45.9336i	−0.893475	+	1.54754i	−0.835681	+	0.549215i	$0.814927\pi$
$882$	7.59550	−	9.28079i	0.255754	−	0.312501i
$883$	−16.5611			−0.557327			−0.278663	−	0.960389i	$-0.589891\pi$
$883$	−16.5611			−0.557327			−0.278663	+	0.960389i	$0.589891\pi$
$884$	5.26488	−	12.4960i	0.177077	−	0.420285i
$885$	42.3524	−	20.0663i	1.42366	−	0.674523i
$886$	11.3753	+	19.7026i	0.382160	+	0.661921i
$887$	24.3148	+	42.1145i	0.816412	+	1.41407i	0.908310	+	0.418299i	$0.137373\pi$
$887$	24.3148	+	42.1145i	0.816412	+	1.41407i	−0.0918974	+	0.995768i	$0.529293\pi$
$888$	0.364131	−	0.172523i	0.0122194	−	0.00578951i
$889$	−20.1796	−	34.9521i	−0.676802	−	1.17226i
$890$	16.4180	+	28.4367i	0.550331	+	0.953201i
$891$	−31.2854	+	27.5871i	−1.04810	+	0.924203i
$892$	14.4318			0.483214
$893$	−25.2003	+	43.6482i	−0.843295	+	1.46063i
$894$	30.9401	+	21.3830i	1.03479	+	0.715153i
$895$	14.4524	+	25.0323i	0.483091	+	0.836738i
$896$	0.569414	−	0.986254i	0.0190228	−	0.0329484i
$897$	−9.98602	+	6.36287i	−0.333423	+	0.212450i
$898$	22.1420	+	38.3511i	0.738888	+	1.27979i
$899$	0.644436	−	1.11620i	0.0214931	−	0.0372272i
$900$	9.81915	−	11.9978i	0.327305	−	0.399927i
$901$	−2.33577	−	4.04568i	−0.0778158	−	0.134781i
$902$	−17.1458	−	29.6974i	−0.570892	−	0.988814i
$903$	1.28825	−	15.8432i	0.0428704	−	0.527230i
$904$	0.556481			0.0185083
$905$	−15.1790	+	26.2908i	−0.504566	+	0.873934i
$906$	3.63694	−	44.7280i	0.120829	−	1.48599i
$907$	57.4045			1.90609			0.953043	−	0.302836i	$-0.0979333\pi$
$907$	57.4045			1.90609			0.953043	+	0.302836i	$0.0979333\pi$
$908$	9.95734	−	17.2466i	0.330446	−	0.572349i
$909$	−10.0038	−	26.4705i	−0.331806	−	0.877973i
$910$	17.2790	−	41.0111i	0.572795	−	1.35950i
$911$	8.77800	+	15.2039i	0.290828	+	0.503729i	0.974006	−	0.226523i	$-0.0727359\pi$
$911$	8.77800	+	15.2039i	0.290828	+	0.503729i	−0.683178	+	0.730252i	$0.739403\pi$
$912$	−4.13956	+	50.9093i	−0.137075	+	1.68577i
$913$	30.5334	+	52.8855i	1.01051	+	1.75025i
$914$	−71.3838			−2.36116
$915$	3.69129	−	45.3964i	0.122030	−	1.50076i
$916$	0.287177	−	0.497406i	0.00948860	−	0.0164347i
$917$	−11.8715	−	20.5621i	−0.392033	−	0.679020i
$918$	18.5599	−	5.34093i	0.612568	−	0.176277i
$919$	19.6019	+	33.9515i	0.646608	+	1.11996i	0.983928	+	0.178567i	$0.0571462\pi$
$919$	19.6019	+	33.9515i	0.646608	+	1.11996i	−0.337320	+	0.941390i	$0.609520\pi$
$920$	−0.331273			−0.0109217
$921$	26.0374	+	17.9946i	0.857962	+	0.592944i
$922$	31.8432	−	55.1540i	1.04870	−	1.81640i
$923$	19.7115	−	46.7844i	0.648812	−	1.53993i
$924$	−32.9860	+	15.6286i	−1.08516	+	0.514143i
$925$	−9.30223			−0.305856
$926$	−32.6227	+	56.5043i	−1.07205	+	1.85685i
$927$	7.87144	+	1.28861i	0.258532	+	0.0423236i
$928$	−13.7975			−0.452925
$929$	5.61374	−	9.72329i	0.184181	−	0.319011i	−0.759119	−	0.650952i	$-0.774370\pi$
$929$	5.61374	−	9.72329i	0.184181	−	0.319011i	0.943300	+	0.331941i	$0.107703\pi$
$930$	0.580663	−	7.14112i	0.0190407	−	0.234167i
$931$	−7.45891	+	12.9192i	−0.244456	+	0.423410i
$932$	−50.7657			−1.66289
$933$	9.84904	−	4.66643i	0.322443	−	0.152772i
$934$	24.4973			0.801577
$935$	23.5629			0.770588
$936$	0.366092	−	0.582601i	0.0119661	−	0.0190429i
$937$	4.40837			0.144015			0.0720076	−	0.997404i	$-0.477059\pi$
$937$	4.40837			0.144015			0.0720076	+	0.997404i	$0.477059\pi$
$938$	55.0825			1.79851
$939$	2.96334	−	36.4438i	0.0967048	−	1.18930i
$940$	−37.5344			−1.22424
$941$	11.3279	−	19.6205i	0.369278	−	0.639609i	−0.620175	−	0.784464i	$-0.712938\pi$
$941$	11.3279	−	19.6205i	0.369278	−	0.639609i	0.989453	+	0.144855i	$0.0462715\pi$
$942$	−26.5694	+	12.5884i	−0.865677	+	0.410154i
$943$	3.49346	−	6.05085i	0.113763	−	0.197043i
$944$	−38.7719			−1.26192
$945$	30.6956	−	8.83319i	0.998527	−	0.287344i
$946$	19.0791	−	33.0461i	0.620317	−	1.07442i
$947$	−3.30435			−0.107377			−0.0536884	−	0.998558i	$-0.517098\pi$
$947$	−3.30435			−0.107377			−0.0536884	+	0.998558i	$0.517098\pi$
$948$	−0.429907	+	5.28709i	−0.0139627	+	0.171717i
$949$	−24.4099	−	32.2136i	−0.792378	−	1.04570i
$950$	−19.1348	+	33.1424i	−0.620814	+	1.07528i
$951$	−1.33553	+	16.4247i	−0.0433077	+	0.532608i
$952$	0.263542			0.00854143
$953$	−26.9889	−	46.7462i	−0.874257	−	1.51426i	−0.857552	−	0.514397i	$-0.828016\pi$
$953$	−26.9889	−	46.7462i	−0.874257	−	1.51426i	−0.0167043	−	0.999860i	$-0.505317\pi$
$954$	−5.37417	−	14.2203i	−0.173995	−	0.460399i
$955$	27.1027	+	46.9433i	0.877024	+	1.51905i
$956$	7.83310	−	13.5673i	0.253341	−	0.438799i
$957$	11.3474	+	7.84224i	0.366808	+	0.253504i
$958$	60.0279			1.93941
$959$	6.65548	+	11.5276i	0.214917	+	0.372246i
$960$	−35.4734	+	16.8071i	−1.14490	+	0.542448i
$961$	15.2187	+	26.3596i	0.490926	+	0.850308i
$962$	−26.2695	+	3.29673i	−0.846962	+	0.106291i
$963$	−0.885778	−	0.145008i	−0.0285438	−	0.00467283i
$964$	30.6536	−	53.0936i	0.987286	−	1.71003i
$965$	29.4848			0.949150
$966$	−12.1409	−	8.39069i	−0.390628	−	0.269966i
$967$	14.3777	−	24.9029i	0.462356	−	0.800824i	−0.536722	−	0.843759i	$-0.680338\pi$
$967$	14.3777	−	24.9029i	0.462356	−	0.800824i	0.999078	+	0.0429352i	$0.0136709\pi$
$968$	−0.666618			−0.0214259
$969$	−21.7102	+	10.2862i	−0.697432	+	0.330440i
$970$	16.9242	+	29.3136i	0.543404	+	0.941203i
$971$	−10.3651	−	17.9530i	−0.332633	−	0.576138i	0.650394	−	0.759597i	$-0.274604\pi$
$971$	−10.3651	−	17.9530i	−0.332633	−	0.576138i	−0.983027	+	0.183459i	$0.941270\pi$
$972$	31.4508	−	3.72625i	1.00878	−	0.119519i
$973$	−15.4178	+	26.7044i	−0.494272	+	0.856104i
$974$	9.98926	+	17.3019i	0.320077	+	0.554389i
$975$	−13.3967	+	8.53608i	−0.429037	+	0.273373i
$976$	−18.8402	+	32.6322i	−0.603060	+	1.04453i
$977$	5.32859	+	9.22938i	0.170477	+	0.295274i	0.938587	−	0.345044i	$-0.112136\pi$
$977$	5.32859	+	9.22938i	0.170477	+	0.295274i	−0.768110	+	0.640318i	$0.778803\pi$
$978$	−6.77824	+	83.3604i	−0.216744	+	2.66557i
$979$	−13.7973	+	23.8977i	−0.440965	+	0.763774i
$980$	−11.1096			−0.354884
$981$	0.751113	+	1.98748i	0.0239812	+	0.0634552i
$982$	3.76747	+	6.52545i	0.120225	+	0.208236i
$983$	−2.52918	−	4.38067i	−0.0806684	−	0.139722i	0.822869	−	0.568231i	$-0.192372\pi$
$983$	−2.52918	−	4.38067i	−0.0806684	−	0.139722i	−0.903537	+	0.428510i	$0.859039\pi$
$984$	−0.0329051	+	0.404675i	−0.00104898	+	0.0129006i
$985$	−27.1583	−	47.0396i	−0.865336	−	1.49881i
$986$	−3.19335	−	5.53104i	−0.101697	−	0.176144i
$987$	−21.4506	−	14.8247i	−0.682781	−	0.471875i
$988$	−21.3115	+	50.5821i	−0.678010	+	1.60923i
$989$	7.77477			0.247223
$990$	75.6698	+	12.3877i	2.40494	+	0.393707i
$991$	25.3039	−	43.8276i	0.803804	−	1.39223i	−0.113292	−	0.993562i	$-0.536140\pi$
$991$	25.3039	−	43.8276i	0.803804	−	1.39223i	0.917096	−	0.398667i	$-0.130527\pi$
$992$	−3.01139	+	5.21588i	−0.0956118	+	0.165604i
$993$	9.79788	−	4.64219i	0.310926	−	0.147315i
$994$	63.2755			2.00698
$995$	25.0517			0.794191
$996$	3.75784	−	46.2147i	0.119072	−	1.46437i
$997$	−23.5181	+	40.7345i	−0.744824	+	1.29007i	0.205453	+	0.978667i	$0.434133\pi$
$997$	−23.5181	+	40.7345i	−0.744824	+	1.29007i	−0.950277	+	0.311406i	$0.899200\pi$
$998$	−28.1236	+	48.7116i	−0.890238	+	1.54194i
$999$	−13.6817	−	13.1874i	−0.432871	−	0.417230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.h.a.22.3	yes	24
3.2	odd	2		351.2.h.a.334.10		24
9.2	odd	6		351.2.f.a.100.3		24
9.7	even	3		117.2.f.a.61.10	✓	24
13.3	even	3		117.2.f.a.94.10	yes	24
39.29	odd	6		351.2.f.a.172.3		24
117.16	even	3	inner	117.2.h.a.16.3	yes	24
117.29	odd	6		351.2.h.a.289.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.10	✓	24	9.7	even	3
117.2.f.a.94.10	yes	24	13.3	even	3
117.2.h.a.16.3	yes	24	117.16	even	3	inner
117.2.h.a.22.3	yes	24	1.1	even	1	trivial
351.2.f.a.100.3		24	9.2	odd	6
351.2.f.a.172.3		24	39.29	odd	6
351.2.h.a.289.10		24	117.29	odd	6
351.2.h.a.334.10		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.00790 q^{2} +(-1.42488 - 0.984744i) q^{3} +2.03168 q^{4} +(-1.37329 + 2.37860i) q^{5} +(2.86102 + 1.97727i) q^{6} +(1.11905 - 1.93825i) q^{7} -0.0636126 q^{8} +(1.06056 + 2.80628i) q^{9} +(2.75743 - 4.77600i) q^{10} +4.63458 q^{11} +(-2.89490 - 2.00069i) q^{12} +(2.17756 + 2.87372i) q^{13} +(-2.24694 + 3.89182i) q^{14} +(4.29908 - 2.03688i) q^{15} -3.93563 q^{16} +(-0.925543 - 1.60309i) q^{17} +(-2.12950 - 5.63475i) q^{18} +(3.74647 + 6.48908i) q^{19} +(-2.79008 + 4.83256i) q^{20} +(-3.50319 + 1.65979i) q^{21} -9.30580 q^{22} +(-0.948030 - 1.64204i) q^{23} +(0.0906403 + 0.0626421i) q^{24} +(-1.27182 - 2.20287i) q^{25} +(-4.37233 - 5.77015i) q^{26} +(1.25230 - 5.04299i) q^{27} +(2.27355 - 3.93791i) q^{28} -1.71833 q^{29} +(-8.63214 + 4.08986i) q^{30} +(-0.375036 + 0.649582i) q^{31} +8.02960 q^{32} +(-6.60372 - 4.56388i) q^{33} +(1.85840 + 3.21885i) q^{34} +(3.07355 + 5.32354i) q^{35} +(2.15472 + 5.70147i) q^{36} +(1.82852 - 3.16709i) q^{37} +(-7.52256 - 13.0295i) q^{38} +(-0.272883 - 6.23903i) q^{39} +(0.0873583 - 0.151309i) q^{40} +(1.84248 + 3.19128i) q^{41} +(7.03407 - 3.33271i) q^{42} +(-2.05024 + 3.55113i) q^{43} +9.41599 q^{44} +(-8.13147 - 1.33118i) q^{45} +(1.90355 + 3.29705i) q^{46} +(3.36320 + 5.82524i) q^{47} +(5.60780 + 3.87559i) q^{48} +(0.995457 + 1.72418i) q^{49} +(2.55370 + 4.42314i) q^{50} +(-0.259845 + 3.19563i) q^{51} +(4.42410 + 5.83847i) q^{52} +2.52368 q^{53} +(-2.51450 + 10.1258i) q^{54} +(-6.36460 + 11.0238i) q^{55} +(-0.0711856 + 0.123297i) q^{56} +(1.05182 - 12.9355i) q^{57} +3.45024 q^{58} +9.85150 q^{59} +(8.73435 - 4.13829i) q^{60} +(4.78708 - 8.29147i) q^{61} +(0.753037 - 1.30430i) q^{62} +(6.62609 + 1.08474i) q^{63} -8.25141 q^{64} +(-9.82583 + 1.23311i) q^{65} +(13.2596 + 9.16383i) q^{66} +(-6.12861 - 10.6151i) q^{67} +(-1.88041 - 3.25696i) q^{68} +(-0.266158 + 3.27327i) q^{69} +(-6.17139 - 10.6892i) q^{70} +(-7.04017 - 12.1939i) q^{71} +(-0.0674649 - 0.178515i) q^{72} -11.2098 q^{73} +(-3.67149 + 6.35922i) q^{74} +(-0.357062 + 4.39124i) q^{75} +(7.61164 + 13.1837i) q^{76} +(5.18632 - 8.98298i) q^{77} +(0.547923 + 12.5274i) q^{78} +(-0.753706 - 1.30546i) q^{79} +(5.40475 - 9.36130i) q^{80} +(-6.75043 + 5.95245i) q^{81} +(-3.69953 - 6.40778i) q^{82} +(6.58818 + 11.4111i) q^{83} +(-7.11736 + 3.37217i) q^{84} +5.08414 q^{85} +(4.11669 - 7.13032i) q^{86} +(2.44841 + 1.69211i) q^{87} -0.294818 q^{88} +(-2.97704 + 5.15639i) q^{89} +(16.3272 + 2.67289i) q^{90} +(8.00677 - 1.00482i) q^{91} +(-1.92609 - 3.33609i) q^{92} +(1.17405 - 0.556260i) q^{93} +(-6.75299 - 11.6965i) q^{94} -20.5799 q^{95} +(-11.4412 - 7.90710i) q^{96} +(-3.06884 + 5.31539i) q^{97} +(-1.99878 - 3.46199i) q^{98} +(4.91524 + 13.0059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

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